Question

Rework Problem 6 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 the motion can be given as$d=-10\sin \left(\frac{2\pi }{3}t\right)$

Step-by-step solution

Given information

We are given$a=10,T=3seconds$

Find the exercise

As the object is moving down the amplitude of the object is $a=10$

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

$$\begin{gathered} \omega =\frac{2\pi }{T} \\ \omega =\frac{2\pi }{3} \end{gathered}$$

Hence the equation can be given as

$d=-10\sin \left(\frac{2\pi }{3}t\right)$

Conclusion

The equation of the motion can be given as$d=-10\sin \left(\frac{2\pi }{3}t\right)$