Chapter 6, Problem 30P

A pair of springs and masses vibrate under simple harmonic motion, as shown in Fig. P6.30. The positions of the masses in inches are given by $y_1\left(t\right)=5\sqrt{2}\cos \left(2\pi t+\frac{\pi }{4}\right)$ and $y_2\left(t\right)=10\cos \left(2\pi t\right)$, 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 $y_1\left(t\right)$.

(b) Plot one cycle of the position $y_1\left(t\right)$, and indicate the earliest time alter $t=0$ when the position is zero.

(c) The vertical distance between the two masses is given by $\delta \left(t\right)=y_1\left(t\right)-y_2\left(t\right)$, Write $\delta \left(t\right)$ in the form $\delta \left(t\right)=M\sin \left(2\pi t+\theta °\right)$ ; in other words, find M and $\theta$.