Question

The equation of a prticle executing simple harmonic motion is `x=(5m)sin[(pis^-1)t+pi/3].` Write down the amplitude time period and maximum speed. Also find the velocity at t=1s.

Answer 1

Comparing with equation `x=Asin(omegat+delta)` se see that
the amplitude `=5m`
and time period `=(2pi)/omega=(2pi)/(pis^-1)=2s`
The maximum speed `=Aomega=5xmmpis^-1=5pims^-1`
the velocity at time `t=(dx)/(dt)=Aomega cos (omegat+delta)`.
At t=1s,
`v=(5m)(pis^-1)cos(pi+pi/3)=-(5pi)/3ms^-1`