Question

An object moves in simple harmonic motion with period 8 minutes and amplitude 15m . At time t=0 minutes, its displacement d from rest is 0 m, and initially it moves in a negative direction. Give the equation modeling the displacement d as a function of time t .

Answer 1

Answer: $d=-15sin\frac{\pi }{4}t$

Step-by-step explanation:

The object is at equilibrium ($d=0$) when $t=0$, so you use the equation $d=asin(x)t$. The amplitude $a$ is 15, and it represents the maximum displacement from 0.

To find $x$, use the formula for the period: $\frac{2\pi }{x}$. The period is 8 minutes, so you set up the formula  $\frac{2\pi }{x}=8$ and solve for $x$.

$x=\frac{\pi }{4}$

Because the object initially moves in a negative direction, the equation should have a negative in front.

Therefore, the answer is $d=-15sin\frac{\pi }{4}t$