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:

$a=10,T=3seconds$

Short answer

The equation of distance is$d=-10\cos \left(\frac{2\pi }{3}\right)$

Step-by-step solution

Given information

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

Find the equation 

The object starts at a position 10 units distance below the resting position so $a=-10$

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

Now we find $\omega$

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

Hence the equation can be given as role="math" localid="1646654788496" $d=-10\cos \left(\frac{2\pi }{3}t\right)$

Conclusion

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