Question

A damped forced oscillation with mass-spring sys- tem is modeled as an nonhomogeneous ODE as following: my" + cy' + ky = r(t) where m = 1 kg, k = 1 N/m and c = 2 N m/s. Initially, y(0) 1m y(0) = -1m/s. r(t) is the input force for this system. Initially (t = (s), there is no input force for this system r(t) = 0 N. At time t = 2s, a costant force (r(t) = 2 N) is applied on the system and it lasts for only 1 second. Later, at time t = 4s, a bullet hits the ball in the mass-spring system, which apples a unit impulse on the system in an instant. Please find the output y(t) of the system and roughly plot it out by hand. hint: you need to solve the differential equation with Laplace Transform

Answer 1

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