A particle moves with simple harmonic motion in a straight line. In first `taus`, after starting form rest it travels a destance a, and in next `tau s` it travels 2a, in same direction, then:

Options

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

Answer

B

Explanation

`cos (omegat) = (A-a)/(A)`
`cos (2omegat) = (A-3a)/(A)`
`rArr (A-3a)/(A) = 2((A-a)/(A))^(2) -1`
`rArr 1-(3a)/(A) = 2+2 ((a)/(2))^(2) -(4a)/(A) -1`
`((a)/(A)) = 2((a)/(A))^(2) A = 2a`
`cos (omegat) = (1)/(2) rArr omegat = (pi)/(3)`
`rArr (2pi)/(T).tau = (pi)/(3) rArr T = 6 tau`