Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): For a particle executing simple harmonic motion, the frequency of its kinetic energy is double the frequency of its displacement. Reason (R): The total mechanical energy of a particle executing simple harmonic motion is directly proportional to the square of its amplitude. In the light of the above

Step-by-step solution

The assertion is true. For a particle in SHM, displacement is given by x = A ( t) and velocity by v = A ( t) . The kinetic energy is K = 1 2 mv^2 = 1 2 mA^2 ^2 ^2( t) . Using the trigonometric identity ^2( ) = 1+ (2 ) 2 , the kinetic energy expression contains a (2 t) term. This means the angular frequency of kinetic energy is 2 , making its physical frequency double that of the displacement. The reason is also true. The total mechanical energy of a particle in SHM is E = 1 2 mA^2 ^2 , which shows it is directly pr