If the spring-mass system has the equation of motion: d?x |dx|dx + a |dt| dt + kx = F, sin(wt) m dt2 Has a value of m = 2 kg , = 5N /(m/s)², and k = 6 N/m. The damping is nonlinear and represents damping from the air. The work function F0 sin(wt) has the values FO %3D = 2.5 N and w = 0.5 rad/sec. Its initial condition when t = 0 s is the initial velocity dx(0)/dt = 0 m/s, and displacement initial x (0) = 1 m . So: c. Draw the velocity versus displacement %3D curve. (note: for this problem do a hand calculation from t = 0 – 5 s, the rest use excel)

A 3 kg object is attached to a spring with spring constant 195 kg/s2. It is also attached to a dashpot with damping constant c = 54 N-sec/m. The object is pushed upwards from equilibrium with velocity 3 m/s. Find its displacement and time-varying amplitude for t > 0. y(t) = sin (3t) + cos (3t) + sin(4t) X The motion in this example is overdamped underdamped. critically damped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t)= 13 cos (wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? What is the maximum possible amplitude?

Find Order,degree and (Linear or -Non Linear)