Chapter 3.5, Problem 19E

To determine

To find:The jerk at time $t$

Answer to Problem 19E

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

Explanation of Solution

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

Calculation:Jerk is third derivative so we find third derivative

Third derivative is:

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

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