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Question:

A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

A/2

A/2√2

A√2

A

Solution:

Potential energy(U)=1/2kx²
Kinetic energy(K)=1/2kA² - x²
According to the question, U=K
∴1/2kx²=1/2kA² - x²
x=±A/√2