Chapter 6, Problem 14P

The position of a spring-mass system shown in Fig. P6.13 is given by $x\left(t\right)=10\sin \left(4\pi t-\frac{\pi }{2}\right)$ cm.

(a) Find the amplitude, frequency, period, and time shift of the position $x\left(t\right)$.

(b) Find the time required for the system to reach $x\left(t\right)=0$ cm and $x\left(t\right)=10$ cm for the first time (after $t=0$ ).

(c) Plot one complete cycle of $x\left(t\right)$, and indicate the amplitude and the time shift on the graph.