First slide

Simple harmonic motion

Question

The potential energy of a particle with displacement X is U(X). The motion is simple harmonic, when (K is a positive constant)

Moderate

A

$U = - \frac{{KX}^{2}}{2}$
B

$U = {KX}^{2}$
C

$U = K$
D

$U = KX$

Solution

$F = - kx$ $\Rightarrow dW = Fdx = - kxdx$
So $\int_{0}^{W} dW = \int_{0}^{x} - kx dx$ $\Rightarrow W = U = - \frac{1}{2} {kx}^{2}$

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