Question

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

• A. \(2\sqrt{A}\)
• B. \(\frac{A}{2}\)
• C. \(\frac{A}{\sqrt{2}}\)
• D. \(A\sqrt{2}\)

Answer 1

The Correct Option is C

In simple harmonic motion (SHM), the total energy (E) is constant and given by E = PE + KE where, PE is potential energy and KE is kinetic energy.

At any displacement (x) from the equilibrium position:

PE = $\frac{1}{2}kx^2$

KE = $\frac{1}{2}k(A^2 - x^2)$

When PE = KE: $\frac{1}{2}kx^2 = \frac{1}{2}k(A^2 - x^2)$

$x^2 = A^2 - x^2$

$2x^2 = A^2$

$x = \frac{A}{\sqrt{2}}$