Chapter 16.2, Problem 69E

(a)

To determine

To calculate: The speed of a moving mass and the direction of motion at times $t=0$ and $t=0.1$ on a spring undergoing damped harmonic motion so that its vertical position at time t seconds is given by $p\left(t\right)=1.2e^{-0.1t}\cos \left(5\pi t+\pi \right)$ centimeters below the rest position.

(b)

To determine

To graph: The functions $p$ and $p^{\prime }$ for t for $0\le t\le 10$ and also for $0\le t\le 1$ and then estimate to the nearest tenth of a second the time at which the velocity of the mass is greatest in downward direction using graphs and graphing technology.