A particle moves with a simple harmonic motion in a straight line, in the first second starting from rest it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the motion is

Options

A. `(2a^(2))/(3a-b)`
B. a-b
C. `2a-b`
D. `a//b`

Answer

A

Explanation

`x=A cos wt` (as it starts from rest at t = 0)
`A - a = A cos w`....(1)
`A - (a+b)=A cos 2w`...(2)
Solving (1) and (2) for A we get `A = (2a^(2))/(3a-b)`.