Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion
During a simple harmonic motion,
Options
- Athe average potential energy over an arbitrary time interval equals the average kinetic energy for that same i
- Bthe potential energy is never equal to the kinetic energy
- Cthe average potential energy over a single time period equals the average kinetic energy for this period
- Dthe potential energy is continuously equal to the kinetic energy
Correct answer
C. the average potential energy over a single time period equals the average kinetic energy for this period
Step-by-step solution
In a simple harmonic motion, the displacement and velocity as functions of time are given by x = A ( t) and v = A ( t) . The instantaneous potential energy is U = 1 2 m ^2 x^2 = 1 2 m ^2 A^2 ^2( t) . The instantaneous kinetic energy is K = 1 2 m v^2 = 1 2 m ^2 A^2 ^2( t) . The average potential energy over one complete time period T is: U = 1 T ₀^ T 1 2 m ^2 A^2 ^2( t) dt = 1 4 m ^2 A^2 The average kinetic energy over one complete time period T is: K = 1 T ₀^ T 1 2 m ^2 A^2 ^2( t) dt = 1 4 m ^2 A^2 Thus, the averag