Question

an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:

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

Short answer

The equation of motion is$d=-4\cos \left(4t\right)$

Step-by-step solution

Given information

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

Find the equation

An object suspended from spring pulled down Hence $a=-4$

Also it starts with amplitude position we will use the cosine function

Now we find $\omega$

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

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

Conclusion

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