
Concept explainers
(a)
The equations of motion of the system shown in Figure P4.90.

Answer to Problem 4.90P
The equations of motion of the system given below,
Explanation of Solution
Given:
The masses are
The spring constant are
Concept used:
Newton’s Second law of motion and Hooke’s Law are used to obtain the equation of motions.
Figure P4.90
Calculation:
Free body diagram of
Applying Newton’s Second law of motion to mass m1
Substituting values for
Substituting values for
Therefore the equations of motion of the system given below,
Where,
(b)
The transfer functions for

Answer to Problem 4.90P
Explanation of Solution
Given:
From part (a),
Concept used:
Laplace Transformation used to obtain the transfer functions.
Assume zero initial conditions for
Calculation:
Converting the equations (1) and (2) to Laplace domain,
for zero initial condition,
from equation (6),
From equation (7) and (5),
From equation (7) and (6),
(c)
A plot of unit step responses of

Answer to Problem 4.90P
Explanation of Solution
Given:
unit-step response of
Solution:
Using MATLAB,
>>sys1=tf([1,0,1000],[20,0,11*10^4,0,3*10^7]);
>> step(sys1)
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Chapter 4 Solutions
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