A particle undergoes simple harmonic motion at a frequency . The frequency at which its kinetic energy oscillates is

Step-by-step solution

Let the displacement of the particle in simple harmonic motion be x = A (2 t + ) . The velocity of the particle is v = dx dt = A(2 ) (2 t + ) . The kinetic energy is given by K = 1 2 mv^2 = 1 2 mA^2(2 )^2 ^2(2 t + ) . Using the trigonometric identity ^2 = 1 + (2 ) 2 , the kinetic energy can be written as: K = 1 4 mA^2(2 )^2 [1 + (4 t + 2 )] The time-varying part of the kinetic energy is (2 (2 )t + 2 ) . This shows that the kinetic energy oscillates with a frequency of 2 .