Question

Consider an undamped spring with spring constant k = 9N/m and with a mass attached with...

Consider an undamped spring with spring constant k = 9N/m and with a mass attached with mass 4kg. We apply a driving force of F(t) = sin(3t/2). Solve the IVP for the position of the mass x(t) with the string initially at rest at the equilibrium (so x(0) = 0 and ˙x(0) = 0). (Hint: Guess a particular solution of the form Ct cos(3t/2) and find the constant C.)

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A body of mass equal to 4 kg is attached to a spring of constant k...
A body of mass equal to 4 kg is attached to a spring of constant k = 64 N / m. If an external force F (t) = 3/2 cos 4t is applied to the system, determine the position and speed of the body at all times; suppose that the mass was in position x (0) = 0.3 m and, at rest, at time t = 0 s
1 Consider an undamped mass-spring system with m = 1, and k = 26, under the...
1 Consider an undamped mass-spring system with m = 1, and k = 26, under the influence of an external force F(t) = 82 cos(ωt). a) (4 points) For what value of ω will resonance occur? b) (6 points) In the case of resonance, solve the initial-value problem with the system assumed initially at rest and briefly discuss what happens.
When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m,...
When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 51e−2t cos 4t  is applied to the system. Find the equation of motion in the absence of damping. x(t)= ?? m
Mass m=1 is attached to a spring with constant k = 4 and dashpot constant c=2....
Mass m=1 is attached to a spring with constant k = 4 and dashpot constant c=2. Suppose the spring is at the equilibrium position resting at time t=0. At t=0 the mass is struck with a hammer with an impulse of 1. Determine the motion of the mass over time (compute for x(t)).
a 3 kg mass is attached to a spring whose constant is 147 N/m, comes to...
a 3 kg mass is attached to a spring whose constant is 147 N/m, comes to rest in the equilibrium position. Starting at  t = 0, a force equal to  f (t)  =  12e−5t cos 2t  is applied to the system. In the absence of damping, (a) find the position of the mass when  t = π. (b) what is the amplitude of vibrations after a very long time?
When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m,...
When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 80e−4t cos 4t is applied to the system. Find the equation of motion in the absence of damping.
Given the undamped spring/mass system The weight is 8 N (Newtons) The spring constant is 100...
Given the undamped spring/mass system The weight is 8 N (Newtons) The spring constant is 100 N/m The length of the spring is 2 m. At t=0, the spring is compressed 0.5 m, making the length 1.5 m. Down is the positive direction A)Determine the frequency of oscillations of the mass? (Include units)   maximum_displacement= B)Determine the equilibrium position including units of the spring with the mass attached (if the mass is not moving.) Equalibrium_position= C)What is the restoring force of...
when a mass of 2 kg is attached to a spring whose constant is 32 N/m,...
when a mass of 2 kg is attached to a spring whose constant is 32 N/m, it come to rest in the equilibrium position. at a starting time t=0, an external force of y=80e^(-4t)*cos(4t) is applied to the system. find the motion equation in the absence of damping.
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. (a) If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response. (b) Find the gain function if the external force is f(t) = cos(ωt). (c) Verify...
A 3.70 kg mass is attached to a spring with a spring constant of 4.06 N/m...
A 3.70 kg mass is attached to a spring with a spring constant of 4.06 N/m . It is initially lifted away from its equilibrium position by 0.200 m in the positive direction and released from rest. A) What is the angular frequency for this oscillator? B) What is the time period for one oscillation for this oscillator? C) Draw out the motion of the oscillator on the graph at the top of the page. ( D) What is the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT