Question

The equation of particle 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 = 1 s`.

Answer 1

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