Chapter 6, Problem 32P

Two oscillating masses are connected by a spring as shown in Fig. P6.32. The positions of the masses in inches are given by $x_1\left(t\right)=5\sqrt{2}\cos \left(2\pi t+\frac{\pi }{4}\right)$ and $x_2\left(t\right)=10\cos \left(2\pi t\right)$, where $t$ is in seconds.

(a) Write down the amplitude, frequency (in Hz), period (in seconds),

phase shift in degrees), and time shift (in seconds) of the position of the first mass $x_1\left(t\right)$.

(b) Plot one cycle of the position $x_1\left(t\right)$, and indicate the earliest time after $t=0$ when the position is zero.

(c) The elongation of the spring is given by $\delta \left(t\right)=x_2\left(t\right)-x_1\left(t\right)$ ,write $\delta \left(t\right)$ in the form $\delta \left(t\right)=M\sin \left(2\pi t+\varphi \right)$ ; in other words, find M and $\varphi$.