(a) The equation of motion of the system.

Question

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Answer 1

Question

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

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Answer 2

Question

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

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Answer 3

Question

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

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Answer 4

Question

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

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Answer 5

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Answer 6

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Answer 7

Chapter 4, Problem 4.52P

To determine

(a)

The equation of motion of the system.

Answer 8

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system are m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 1

Figure-(1)

Write the equation of motion for mass 1.

m1x1+cx1+k(x1−x2)=0m1x1=−cx1−k(x1−x2)m1x1=−cx1+k(x2−x1) ...... (I)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k(x2−x1)=fm2x2=f−k(x2−x1) ...... (II)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1+k(x2−x1) and m2x2=f−k(x2−x1).

Answer 13

To determine

(b)

The equation of motion of the system.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Answer 14

To determine

(b)

The equation of motion of the system.

Answer 15

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The figure below shows the free body diagram of the block 1 and 2.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 2

Figure-(2)

Write the Equation of motion for mass 1.

m1x1+kx1+c(x1−x2)=0m1x1=−kx1−c(x1−x2)m1x1=−kx1+c(x2−x1)=0 ........ (III)

Here, mass of body 1 is m1, damping coefficient is c, spring constant is k, displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the equation of motion for mass 2.

m2x2+c(x2−x1)=fm2x2=f−c(x2−x1) ...... (IV)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−kx1+c(x2−x1)=0 and m2x2=f−c(x2−x1).

Answer 20

To determine

(c)

The equation of motion.

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Answer 21

To determine

(c)

The equation of motion.

Answer 22

Expert Solution

Answer to Problem 4.52P

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

The damping coefficient is c and friction is negligible.

The Figure below shows the free body diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 3

Figure-(3)

Write the equation of motion for mass 1.

m1x1+cx1+k1x1+k2(x1−x2)=0m1x1=−cx1−k1x1−k2(x1−x2)m1x1=−cx1−k1x1+k2(x2−x1)=0 ........ (V)

Here, mass of body 1 is m1, damping coefficient is c, spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, and the displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+k2(x2−x1)=fm2x2=f−k2(x2−x1) ...... (VI)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−cx1−k1x1+k2(x2−x1)=0 and m2x2=f−k2(x2−x1).

Answer 27

To determine

(d)

The Equation of motion.

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.

Write the Equation of motion for mass 2.

m2x2+c2(x2−x1)+k2(x2−x1)=fm2x2=f−c2(x2−x1)−k2(x2−x1) ...... (VIII)

Here, mass of body 2 is m2 and the input force is f.

Conclusion:

The equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Answer 28

To determine

(d)

The Equation of motion.

Answer 29

Expert Solution

Answer to Problem 4.52P

The Equation of motion of the system is m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) and m2x2=f−c2(x2−x1)−k2(x2−x1).

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given information:

The damping coefficient of damper 1 is c1, the damping coefficient of damper 2 is c2.

The figure below shows the free diagram of the system.

System Dynamics, Chapter 4, Problem 4.52P , additional homework tip 4

Figure-(4)

Write the Equation of motion for mass 1.

m1x1+c1x1+k1x1+c2(x1−x2)+k2(x1−x2)=0m1x1=−c1x1−k1x1−c2(x1−x2)−k2(x1−x2)m1x1=−c1x1−k1x1+c2(x2−x1)+k2(x2−x1) ........ (VII)

Here, mass of body 1 is m1, damping coefficient of first damper is c1, damping coefficient of second damper is c2 spring constant for first spring is k1, the spring constant for spring 2 is k2 displacement of mass1 is x1, displacement of mass 2 is x2.