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
$kinetic energy of simple harmonic oscillator is = K= \frac{1}{2} {mω}^{2} {(A}^{2} {-x}^{2}) W h e n x = 0, K = \frac{1}{2} {mω}^{2} {(A}^{2}) this is maximum energy p o t e n t i a l energy of simple harmonic oscillator is = PE= = \frac{1}{2} {mω}^{2} {(x}^{2}) W h e n x = 0, P E = 0 t o t a l e n e r g y o f a s i m p l e h a r m o n i c o s c i l l a t o r = T E = \frac{1}{2} {mω}^{2} {(A}^{2}) = c o n s \tan t$

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