Question

A simple harmonic motion is represented by
`x=10sin(20t+0.5).`
Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time seconds.

Answer 1

Given, `y=10sin(20t+0.5)`
Comparing it with the displacement in SHM
`y=Asin(omegat+phi_(0))`
we get, (i) Amplitude, `A=10m`
(ii) Amgular frequency, `omega=20rads^(-1)`
(iii) Frequency, `v=(omega)/(2pi)=(20)/(2xx22//7)=3.18Hz`
(iv) Time period, `T=(2pi)/(omega)=(2xx22//7)/(20)=0.314s`
(v) Initial phase, `phi_(0)=0.5rad`