Chapter 5.CR, Problem 76CR

To determine

(a)

To Graph:

The given function $y=\frac{\pi }{8}\cos \left[3\pi \left(t-\frac{1}{3}\right)\right]$ with respect to t.

To determine

(b)

The velocity and acceleration of the arm for the given function $y=\frac{\pi }{8}\cos \left[3\pi \left(t-\frac{1}{3}\right)\right]$.

To determine

(c)

To prove:

The equation $\frac{d^{2}y}{d{t}^2}+9{\pi }^{2}y=0$ has related to angle y and the acceleration.

To determine

(d)

To find:

The direction of the force at $t=1\text{ second}$, $t=\frac{4}{3}\text{ seconds}$, and $t=\frac{5}{3}\text{ seconds}$, and also position of the arm at each times.