Suppose a spring with spring constant 2 N/m is horizontal and has one end attached to a wall and the other end attached to a 4 kg mass. Suppose thatthe friction of the mass with the floor (i.e., the damping constant) is 1 N. s/m, and the forcing function is F(t) = 2 cos(2t).Determine the steady-state response of the system.Ysteady-statehelp (formulas)

Answered: Image /qna-images/answer/71c9b66f-b2f2-4f57-8b89-52b015253d36.jpg

Answered: Suppose a spring with spring constant 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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After a mass weighing 8 pounds is attached to a 5-foot spring, the springmeasures 6.6 feet. The entire system is placed in a medium that offersa damping constant of one.Find the equation of motion if the mass is initially released from a point 6inches above the equilibrium position with a downward velocity of1 ft/sec
The "Yaw Damper System" provides airplane stabilization about the yaw axis. The Yaw Damper minimizes dutch roll during flight by providing rudder displacement proportional to, and opposing, the yaw rate of the airplane. Transfer function of the yaw damper is taken as: 4.833 yaw rate rudder angle (s+0.551)(s+0.1 ±0.541*i) (s+0.616)(s +0.058+ i)(s+0.007) a) Give a brief knowledge about yaw dampers. b) Draw and interpret "root-locus" graphic of this transfer function. c) Draw and interpret the yaw rate distribution according to time.
In the system shown, m = 4 kg, 0 = 40°, µ¸ = 0.5 and µk = 0.3 and the wheels are frictionless. (a) Determine the maximum value of force P for the system to have static equilibrium. Call this force Pmax (Pmax = 105.7 N) (b) Determine the force P for the system to have dynamic equilibrium, that is, moves with constant velocity, while moving up the incline. (P = 93.7 N) = 2Pmax, determine the accel- (c) If the system is released from rest with the cable taught and P eration of the bodies and the tension of the cable. (a = 9.81 m/s², T = 147 N) μς, μκ < 2m Ꮎ m P
Solute the question 4and 5，please
Consider a spring-mass system that has a 15 kg mass, a damping coefficient of 45 N/m², and a spring that, when stretched 0.4 m, imposes a force of 12 N. a.) Explain why the spring constant is 30 N/m. 45 b.) These values lead to the equation, y + 15y + 3y = 0, assuming no forcing function is present. Solve for the position as a function of time by using an appropriate guess. Be sure to show all work. (You can round to two decimal places, e.g., 94.3453 = 94.35) c.) Now, suppose we incorporate a forcing function of e-2t, such that our equation becomes y" + 3y + 2y = e 2t. We might imagine our particular guess to be of the form ae 2t, however, it will not work in this case. So, use a guess of the form ypat e 2t. With this, apply the Linearity Principle to find the general solution to this nonhomogeneous ODE.

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