First slide

Simple harmonic motion

Question

A body executes simple harmonic motion. The potential energy (PE), kinetic energy (KE) and total energy (TE) are measured as a function of displacement x. Which of the following statement is true?

Moderate

A

TE is zero when x = 0
B

PE is maximum when x = 0
C

KE is maximum when x = 0
D

KE is maximum when x is maximum

Solution

$\begin{array}{l} y = x \\ P E = \frac{1}{2} m ω^{2} y^{2} \\ K E = \frac{1}{2} m ω^{2} (a^{2} - y^{2}) \\ T E = P E + K E = \frac{1}{2} m ω^{2} a^{2} \end{array}$
Since PE is maximum at x = a and KE is maximum at x = 0, therefore TE remains constant throughout the motion.

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