A particle executes `S.H.M` ina straight line. In the first second starting from rest it travels a distance `'a'` and in the next second a distance `'b'` in the same direction. The amplitude of `S.H.M.` will be

Options

A. ` a - b `
B. ` ( 2 a - b ) / ( 3 ) `
C. ` (2a ^ 2 ) /( 3a - b ) `
D. None

Answer

C

Explanation

Starting from extreme position
` x = A cos omega t `
` a = A - x `
` a = A - A cos omega " " `…(1)
` a + b = A - A cos 2 omega " " `…(2)
Solve equation (1) and (2)