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(\pi )/(4)t`

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:
`(2\pi )/(x)`. The period is 8 minutes, so you set up the formula
`(2\pi )/(x)=8` and solve for
`x`.

`x=(\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(\pi )/(4)t`