The potential energy of a simple harmonic oscillator when the particle is at 3 4 A , is ( A is the amplitude of oscillation and E is the total energy of the oscillator)

Step-by-step solution

The potential energy of a simple harmonic oscillator at a displacement x is given by U = 1 2 k x^2 . The total energy of the oscillator is E = 1 2 k A^2 . Given the displacement x = 3 4 A , substituting this into the potential energy formula gives: U = 1 2 k ( 3 4 A )^2 U = 9 16 ( 1 2 k A^2 ) Since E = 1 2 k A^2 , we get: U = 9 16 E Answer: 9 16 E