Question

A m=5 kg mass hangs on a spring that is stretched 2 cm under the influence...

A m=5 kg mass hangs on a spring that is stretched 2 cm under the influence of the weight of this mass. The mass is attached to a damper with a damping constant of c=200 Ns/m. A periodic external force of F(t) = 200cos(ωt) is now applied on the mass that was initially in static equilibrium. Neglecting any friction, obtain a relation for the displacement of the mass x(t) as a function of ω and t. Also, determine the value of ω that will cause resonance to occur.

This is a combined question from the book of Differential Equations for Engineers and Scientists by Cengel. Question 3-195 and 3-198 is mixed.

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
A spring with spring constant 4 N/m is attached to a 1kg mass and a dashpot...
A spring with spring constant 4 N/m is attached to a 1kg mass and a dashpot with damping constant 4 Ns/m.A periodic force equal to 2 cos(t) N is applied to this system. Assume that the system starts withx(0) = 1 andx′(0) = 2,
A mass m=0.65 kg hangs at the end of a vertical spring whose top end is...
A mass m=0.65 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has a constant K=85 N/m and negligible mass. At time t=0 the mass is released from rest at a distance d=0.35 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by  y(t) = A cos(ωt – φ). The positive y-axis point upward. Part (b) Determine the value of the...
A mass of 2 kg. is attached to a spring with spring constant k = 17/2...
A mass of 2 kg. is attached to a spring with spring constant k = 17/2 and damping constant of magnitude 2, with no external force.If the initial displacement is 2 m and the initial velocity is 3 m/s, find the position u(t) of the mass for any time t > 0. Graph u vs t in Desmos and attach a screenshot.
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.
A mass m = 1.4 kg hangs at the end of a vertical spring whose top...
A mass m = 1.4 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 75 N/m and negligible mass. At time t = 0 the mass is released from rest at a distance d = 0.35 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y(t) = A cos(ωt – φ). The positive y-axis...
Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring...
Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring is 18 N/m, and the external force is a periodic force f(t) = 6sin(3t): a) Write the differential equation modeling the motion of this spring-mass system b) Solve the differential equation in (a). Show Work c) If at the initial time t = 0, the mass is at position 2 m to the right of the equilibrium position and its velocity is 1 m/s...
A 5​-kg mass is attached to a spring with stiffness 225 N/m. The damping constant for...
A 5​-kg mass is attached to a spring with stiffness 225 N/m. The damping constant for the system is 30√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 3 ​m/sec, what is the maximum displacement from equilibrium that it will​ attain? ​(Type an exact​ answer, using radicals as​ needed.)
A 1/2 kg mass is attached to a spring with 20 N/m. The damping constant for...
A 1/2 kg mass is attached to a spring with 20 N/m. The damping constant for the system is 6 N-sec/m. If the mass is moved 12/5 m to the left of equilibrium and given an initial rightward velocity of 62/5 m/sec, determine the equation of motion of the mass and give its damping factor, quasiperiod, and quasifrequency. What is the equation of motion? y(t)= The damping factor is: The quasiperiod is: The quasifrequency is:
A 1-kg mass is attached to a spring whose constant is 16 N/m and the entire...
A 1-kg mass is attached to a spring whose constant is 16 N/m and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equation if (A) The weight is released 60 cm below the equilibrium position. x(t)= ; (B) The weight is released 60 cm below the equilibrium position with an upward velocity of 17 m/s. x(t)= ; Using the equation from part b, (C)...
A simple pendulum with mass m = 2 kg and length L = 2.67 m hangs...
A simple pendulum with mass m = 2 kg and length L = 2.67 m hangs from the ceiling. It is pulled back to an small angle of θ = 11° from the vertical and released at t = 0. 1)What is the period of oscillation? s   2)What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N   3)What is the maximum speed of the pendulum? m/s   4)What is the angular displacement at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT