Question

differential equations: a 2kg mass is placed on a spring with k=8. at t=0, the system...

differential equations:

a 2kg mass is placed on a spring with k=8. at t=0, the system is set in motion from its equilibrium position by an external force given by 2cos(wt) where w is a positive constant. for which value of w, if any, will the system have resonance?
Math   Advanced-Math   
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
Differential Equations A spring is stretched 6in by a mass that weighs 8 lb. The mass...
Differential Equations A spring is stretched 6in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb· s/ft and is acted on by an external force of 2cos(2t) lb. (a) Find position u(t) of the mass at time t (b) Determine the steady-state response of this system Assume that g = 32 ft/s2
A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes...
A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes to rest at its equilibrium position. The spring constant is 9 lb/ft and there is no damping. A. How far (in feet) does the mass stretch the spring from its natural length? L=________ (do not include units). B. What is the resonance frequency for the system? ?0= _________(do not include units). C. At time t=0 seconds, an external force F(t)=2cos(?0t) is applied to the...
A 2kg mass is attached to a spring with stiffness k = 8π2N/m. The mass is...
A 2kg mass is attached to a spring with stiffness k = 8π2N/m. The mass is displaced 1m to the right of the equilibrium and given a velocity of 2π m/sec to the right. No damping and no external for are assumed. (a) Find the period and the frequency of the motion (with appropriate units). (b) Write the displacement y(t) of the mass in phase-amplitude form (every computation must be shown). (c) What is the maximum displacement from the equilibrium...
A mass m is attached to a spring with stiffness k=25 N/m. The mass is stretched...
A mass m is attached to a spring with stiffness k=25 N/m. The mass is stretched 1 m to the left of the equilibrium point then released with initial velocity 0. Assume that m = 3 kg, the damping force is negligible, and there is no external force. Find the position of the mass at any time along with the frequency, amplitude, and phase angle of the motion. Suppose that the spring is immersed in a fluid with damping constant...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches. If the weight is released from rest at a point 4 inches below the equilibrium position, the system is immersed in a liquid that offers a damping force numerically equal to 3 times the instantaneous velocity, solve: a. Deduce the differential equation that models the mass-spring system. b. Calculate the displacements of the mass ? (?) at all...
A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by...
A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by an external force of 4 cos(t) N. If the mass is set in motion from its equilibrium position with a downward velocity of 2 m/s, find the position of the mass at any time. Identify the transient (i.e., complementary) and steady state (i.e., particular) solutions. Does the motion exhibit resonance or a beat?
We consider a spring mass system. We use standard international system of units, the mass is...
We consider a spring mass system. We use standard international system of units, the mass is 1kg and the change of magnitude of force |∆Fs| (in unit of Newton, 1N = 1kg ∗ m/s2) from the spring is 9 times the change of length of the spring |∆x|(in meter), i.e |∆Fs| = |9∆x|, the spring is a linear spring with spring constant equal to 3 in Hook’s law. The equilibrium position is at x = 0. When the external forcing...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches. If the weight is released from rest at a point 4 inches below the equilibrium position, and the entire system is immersed in a liquid that imparts a damping force numerically equal to 3 times the instantaneous velocity, solve: a. Deduce the differential equation that models the mass-spring system. b. Calculate the displacements of the mass ? (?)...
.1.) Modelling using second order differential equations a) Find the ODE that models of the motion...
.1.) Modelling using second order differential equations a) Find the ODE that models of the motion of the dumped spring mass system with mass m=1, damping coefficient c=3, and spring constant k=25/4 under the influence of an external force F(t) = cos (2t). b) Find the solution of the initial value problem with x(0)=6, x'(0)=0. c) Sketch the graph of the long term displacement of the mass m.
A mass on a spring undergoes simple harmonic motion. At t = 0 its displacement is...
A mass on a spring undergoes simple harmonic motion. At t = 0 its displacement is 1m and its velocity is 1m/s towards the equilibrium position. What single piece of information allows you to determine the displacement at time t = 1 s? A. mass B. spring constant (k) C. kinetic energy at t = 0 D. acceleration at t = 0 E. force at t = 0
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT