!!!!!!!!!oscillation problem..!help me please!!!?

Question

A mass m is attached on a horizontal spring and is immobile.The k of the spring is 2000 N/m.We move the mass away from the equillibrium point to an amplitude A'=0.16 cm and then we set it free to move.It does a damped oscillation, with an amplitude which is getting smaller 25% in evey oscillation.

Find how much will the total energy be decreased after the two first oscillations of the mass.

Answer 1

Initial kinetic energy KEi = k/2*amplitude^2. After 2 cycles KEf = KEi*0.75^2. The reduction deltaKE = KEi - KEf = KEi*(1-0.75^2). The PE of the statically deflected spring remains unchanged so the total E reduction = deltaKE.