Question

Assume an object with mass m=1 kg is attached to a spring with stiffness k=2 N/m and lies on a surface with damping constant b= 2 kg/s. The object is subject to the external force F(t) = 4cos(t) + 2sin(t). Suppose the object starts at the equilibrium position (y(0)=0) with an initial velocity of y_1 (y'(0) = y_1).

In general, when the forcing function F(t) = F*cos(γ*t) + G*sin(γ*t) where γ>0, the solution is the sum of a periodic function y_p(t) and a nonperiodic function y_c(t), where "limit(y[c](t), t = infinity) = 0". In this case we call y_c(t) the transient solution and y_p(t) the steady-state solution. Using the solution you found in part (b) for when y_1=7, find both the transient and steady-state solutions for y(t) and plot them both in Maple along with y(t). At approximately what t-value does y(t) equal the steady-state solution?

Answer 1