Chapter 6, Problem 33P

Now assume that the positions of two masses in problem P6-31 are given by $x_1\left(t\right)=8\sin \left(4\pi t+\frac{\pi }{4}\right)$ and $x_1\left(t\right)=8\sin \left(4\pi t+\frac{\pi }{4}\right)$, 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) Write $\delta \left(t\right)=x_2\left(t\right)-x_1\left(t\right)$ in the form $\delta \left(t\right)=M\cos \left(4\pi \pi t+\varphi \right)$ ; in other words, find M and $\varphi$.