First slide

Simple harmonic motion

Question

The potential energy of a particle $(U_{x})$ executing SHM is given by

Moderate

A

$U_{x} = \frac{K}{2} {(a - x)}^{2}$
B

$U_{x} = K_{1} x + K_{2} x^{2} + K_{3} x^{3}$
C

$U_{x} = A e^{- b x}$
D

$U_{x} = a constant$

Solution

PE of body in SHM at an instant
$PE=U = \frac{1}{2} m ω^{2} y^{2} = \frac{1}{2} K y^{2}$
m is mass of oscillator, $ω$ is angular velocity, y is displacement of oscillator, k is force constant
If the displacement , $y = (a - x)$ then
$U = \frac{1}{2} K {(a - x)}^{2} = \frac{1}{2} K {(x - a)}^{2}$

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