Point A moves with a constant velocity vo. It is connected to a particle of mass m by a linear damper whose tensile force is F = c(vo - x). (a) Assuming the initial conditions x(0) = 0, (0) = 0, solve for the particle velocity i as a function of time. (b) Find the work W done on the system by the force F acting on A. (c) Show that the work W approaches twice the value of the kinetic energy T as time t approaches infinity. %3D %3D

Point A moves with a constant velocity vo. It is connected to a particle of mass m by a linear damper whose tensile force is F = c(vo - x). (a) Assuming the initial conditions x(0) = 0, (0) = 0, solve for the particle velocity i as a function of time. (b) Find the work W done on the system by the force F acting on A. (c) Show that the work W approaches twice the value of the kinetic energy T as time t approaches infinity. %3D %3D

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The system shown below is released from rest and slider B moves to the right with the constant…

Q: The 3.55 kg collar shown below is attached to a spring and released from rest at A. The collar then…

A: Given data:Mass of collar:m= 3.55 kgSpring constant : k= 22.5 N/mDistance of a = 1.15 mDistance of Y…

Q: As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The…

A: Apply conservation of momentum. mv=mv6+Mv'v'=5mv6M

Q: Plz solve correctly

A: Part (a): Finding the Speed of the 10-kg BlockInitially, the system is at rest, so the total…

Q: The motor exerts a constant force of T (N) on the cable. The final speed of the will define the…

A: When there is any relative motion between any two surfaces, there is a force that opposes the motion…

Q: M= 2,500 kg m= 800 kg

Q: A spring is stretched 3 cm by a force of 6 N. Thus, according to Hooke's Law, the spring DO = 200 N.…

A: From the conservation of energy, the initial kinetic energy of the mass is equal to the final…

Q: A car m = 200 tons makes the journey shown in the figure, if it moves with an initial speed of…

A: Based on diagram, trajectory is assumed to be an hemisphere with radius 15000 m. FBD:

Q: Oblique Impact To analyze an oblique impact using the conservation of momentum and coefficient of…

A: From the given vector diagram, The velocity components in the x-direction are given as, After…

Q: A vertical spring with a mass attached at its end stretches by an amount 20 cm before coming to…

A: As we know that spring is a resilient body which try to restore the body to natural length of it…

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

1.8. Point A moves with a constant velocity vo. It is connected to a particle of mass m
by a linear damper whose tensile force is F = c(vo – x). (a) Assuming the initial
conditions x(0) = 0, i(0) = 0, solve for the particle velocity i as a function of time.
(b) Find the work W done on the system by the force F acting on A. (c) Show that
the work W approaches twice the value of the kinetic energy T as time t approaches
infinity.
Problems
y=vot
Figure P 1.8.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

4. A spring with stiffness constant k = 2000 N/m attached to a platform launched a mass of 2kg vertically in the air to some maximum height (measured from the equilibrium point of the spring). The spring was compressed by 0.3 meters before launch. Due to internal friction of the spring, 10 Joules of energy was lost as the spring expanded. How fast was the mass travelling when it was at half of its maximum height? You must use g= 10m/s? for this problem or you will actually find it much more difficult to calculate. Hint: First solve the problem of finding what the maximum height is and then solve the problem of finding the speed at half of that height.
QI) Two masses m, = 2 kg and m2 = 8 kg are attached to each other by a string passing through a massless pulley of radius R = 1m. m, is also attached to vertical spring of stiffness constant k = 20 N/m and equilibrium length 3h = 6m, while m2 is held at a height of h = 2m initially. If the system is released from rest, a) Find the speed of the blocks right before m2 hits the ground. m1 m2 3h h b) Repeat the question for the case where the pulley has a mass, hence a moment of inertia I = 30 kg · m².
The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denoted
1) Is it possible to prescribe the velocity v0, so that the pendulum keeps rotating with alpha = pi/2 Explain clearly why? Given: L, g, and m. 2) After transient motion, the pendulum settles at steady state rotation atalpha = pi/3. Find the initial velocity v0. Given: L, g, m, sin(pi/3) = (squareroot(3)/2), cos(pi/3) = (1/2). [Hint: Use the conservation of energy and the 2nd Newton’s law.]
I need help on this problem.
Consider a system of three masses, each with mass m, joined by ideal, massless springs, each with spring's constant k, as shown in figure 1. k m x1 k m x2 k m X3 k Figure 1: 3 identical masses attached with identical ideal, massless springs. The coordi- nates 1, 2, 3 represent the position in time of each of the masses. Neglect any effect due to gravity. (a) Show the spring forces acting upon each mass when T1, T2, T3 > 0. (b) Find the equations of motion of each mass. That is, a system of second order, coupled differential equations for x1, x2, x3. (c) Find the normal modes of the system and their associated angular frequencies.
A fender is mounted on a automobile though dampers (to absorb collision energy) and springs (so that the fender can recover after low-speed collisions). During a crash-test, the automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The springs that mount the fender have a stiffness, k, of 1,000,000 N/m. y m barrier 1) Write a differential equation for the deflection of the springs when the fender is in contact with the barrier. 2) If the damping coefficient, c, is 30,000 N-s/m, what is the damping ratio of the mass-spring-damper system when the fender is in contact with the barrier? 3) For that damping coefficient, make a reasonably accurate sketch (with properly labeled axes) of the time-course of the force exerted on the barrier, starting from the moment of first contact. 4) Is there any value of the damping coefficient, c, that would yield no rebound of the vehicle from…
8.3 classic mechanics please provide a solution for the following
A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 2 inches above the equilibrium position. Give the initial conditions. (Use g 32 ft/s? for the acceleration due to gravity.) x(0) X ft %3D x'(0) ft/s Find the equation of motion. x(t) X ft Need Help? Read It Watch It
A 25 kg mass is attached to a spring with spring constant 100 N/m. The mass is driven by an external force equal tof(t) = 5 cos(2t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.) Write the initial-value problem which describes the position of the mass.
k k F Two masses, m¡ and m2 are attached in series by two springs. A force, F is applied to the second mass. Each spring has spring constant, k. The position of each mass is described by x1 and x2, where Fspring 1 = -kx1 and Fspring 2 = -k(x2 – x1) 1. write out the kinetic and potential energy in terms of x1 and x2 2. Use the Lagrange equations to write out two coupled ordinary differential equations here, the force F does virtual work, F8x2
A Rod with mass m and length L can rotate freely about one of its ends. A point mass with the same mass as the rod (m) can move freely along the length of the rod (ignore friction). The point mass is attached to a spring with a spring constant K and a negligible initial length. Gravity acts. Use Newton's Second Law (this includes the torque equation if you need it) and derive the Equation(s) of motion for this system. L mu K m m