A particle moves with simple harmomonic motion in a straight line. In first `tau s`, after starting from rest it travels a distance a, and in next `tau s` it travels 2a, in same direction, then :-

Options

A. amplitude of motion is `3a`
B. time period of oscillations is `8tau`
C. amplitude of motion is `4a`
D. time period of oscillations is `6tau`

Answer

D

Explanation

`x = Acosomegat`
displacement in `t` time `= A - Acosomegat`
for `t = tau , A[1 - cos omegatau] = a`
for `t = 2tau`
`A[1 - cos 2omgatau] = 3a`
`(1 - cos omegat)/(1 - cos2omegat) = (1)/(3)`
`(1 - cos omegatau)/(1 - cos2omegatau) = (1)/(3)`
Say `x = cosomegat`
`(1 - x)/(2(1 - x^(2))) = (1)/(3)`
`rArr 3 = 2 + 2x rArr x = (1)/(2) = cos omegatau`
`A = 2a, omegatau = (pi)/(3) rArr (2pi)/(T) tau = (pi)/(3) rArr T = 6tau`