Question

An object moves in simple harmonic motion with amplitude 14cm and period 0.2 seconds. At time =t0 seconds, its displacement d from rest is 0cm, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time t.

Answer 1

d= 14 sin 31.41 t

Step-by-step explanation:

Lets take the general equation of the motion

d= D sinωt

d=Displacement

ω=Natural angular frequency

t=Time

D=Amplitude

Given that D= 14 cm

We know that time period T

`T=(2\pi)/(\omega)`

Given that T= 0.2 s

`0.2=(2\pi)/(\omega)`

ω=31.41 rad/s

D= 14 cm

Therefore

d= D sinωt

d= 14 sin 31.41 t