Chapter 10, Problem 42P

A biomedical engineer is designing a resistive training device to strengthen the latissimus dorsi muscle. The task can be represented as a spring-mass system, as shown in Fig. P10.28. The displacement $y\left(t\right)$ of the exercise bar satisfies the second-order differential equation

$m\ddot{y}\left(t\right)+ky\left(t\right)=f\left(t\right)$.

Subject to the initial condition $y\left(0\right)=0.01\text{m}$ and $\stackrel{\dot{}}{y}\left(0\right)=0\text{m/s}$.

(a) Determine the transient solution $y_{tran}\left(t\right)$.

(b) Determine the steady-state solution $y_{ss}\left(t\right)$ for the applied force shown in Fig. P10.42.

(c) Determine the total solution, subject to the initial conditions.