A particle having mass 10 g oscillates according to the equation `x=(2.0cm) sin[(100s^-1)t+pi/6]`. Find a the amplitude the time period and the spring constant b. the position, the velocity and the acceleration at t=0.

Answer

(a) `2.0 cm, (pi)/(50)s = 0.063 s, 100 N//m` (b) `1.0 cm, sqrt(3) m//s, 100 m//s^(2)`

Explanation

`x = (2.0 cm) sin [(100s^(-1))t + (pi)/(6)]`
Compare this equation with
`x = A sin (omega t + phi) rArr A = 2.0 cm`
`T = (2pi)/(3) = (2pi)/(100) = 0.0635`
`K = momega^(2) = (10)/(100) 100^(2) = 100 N//m`
`x_(t = 0) = 2.0 sin [100 xx 0 + (pi)/(6)] = 1 cm`
`v = 200 cos (100t + (pi)/(6))`
`v = 200 cos (100t + (pi)/(6))`
`v_(t = 0) = 200 cos (100 xx 0 + (pi)/(6)) = 100sqrt(3) cm//s = sqrt(3) m//s`
`a = 2000 sin (100 xx 0 + (pi)/(6)) = 10000 cm//s^(2) = 100 m//s^(2)`