First slide

Simple harmonic motion

Question

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

Moderate

A

KE is maximum when x=0
B

TE is zero when x=0
C

KE is maximum when x is maximum
D

PE is maximum when x=0

Solution

At x=0, KE is maximum and PE is minimum
$∴ KE= K= \frac{1}{2} {mω}^{2} {(A}^{2} {-x}^{2})$ here m = mass of oscillator, w= angular frequency,A= amplitude, x= displacement of oscillator
When x=0, $K= \frac{1}{2} {mω}^{2} A^{2}$ = (maximum)
And at x=0, $PE= \frac{1}{2} {mω}^{2} x^{2}$ =0 (minimum)
So KE is maximum at x=0.

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