Question

Rework Problem 8 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.

Short answer

The equation of object can be given as$d=-4\sin \left(4t\right)$

Step-by-step solution

Given information

We are given$a=4,T=\frac{\pi }{2}seconds$

Find the equation

As the object is moving down the amplitude of the object is $a=4$

Since at t=0 the object is at resting position and moving downward we will use$-\sin$

in the equation

The angular velocity can be given as

$$\begin{gathered} \omega =\frac{2\pi }{T} \\ \omega =\frac{2\pi }{{\displaystyle \frac{\pi }{2}}} \\ \omega =4 \end{gathered}$$

Hence the equation of the object can be given as$d=-4\sin \left(4t\right)$

Conclusion

The equation of the object can be given as$d=-4\sin \left(4t\right)$