A particle performs `SHM` of amplitude `A` along a straight line .When it is a distance `sqrt(3)/(2)`A from mean position its kinetic energy gets increase by on amount `(1)/(2) m omega^(2)A^(2)` due to an implusive force. Then its new amplitude because

Options

A. `sqrt(5)/(2)A`
B. `sqrt(3)/(2)A`
C. `A`
D. `sqrt(2)A`

Answer

C

Explanation

Due to impulse the total energy of the particle becomes
`(1)/(2) m omega^(2) A^(2) + (1)/(2)m omega^(2) A^(2) = m omega^(2) A^(2)`
Let `A` be the new amplitude
`:. m omega^(2) (A)^(2) = m omega^(2) A^(2)`
`rArr A' = A`.