# A particle performs Simple harmonic motion of amplitude A along a straight line. When it is at a distance 31/2/2 A from mean position its kinetic energy gets increased by an amount 1/2 mw2A​2 due to an impulsive force. Then it's new amplitude becomes what?

Dear Student,

If the particle performs SHM with amplitude A along the straight line, than at any point the total energy should be,

$E=K+P=\frac{1}{2}K{A}^{2}=\frac{1}{2}m{\omega }^{2}{A}^{2}$.
If the additional kinetic energy of magnitude $\frac{1}{2}m{\omega }^{2}{A}^{2}$ by means of an impulsive force, then the total energy of the particle changes to,