Chapter 3.5, Problem 20E

To determine

To find:The jerk at time $t$

Answer to Problem 20E

The jerk at time $t$ is $-2\cos t$ .

Explanation of Solution

Given information:A body is moving in simple harmonic motion with position function $s=2+2\sin t$ .

Calculation:Jerk is third derivative so we find third derivative

Third derivative is:

  $\begin{array}{l}s=2+2\sin t\\ s\text{'}=2\cos t\\ s\text{'}\text{'}=2(-\sin t)=-2\sin t\\ s\text{'}\text{'}\text{'}=-2(\cos t)=-2\cos t\end{array}$

Therefore the jerk at time $t$ is $-2\cos t$ .