First slide

Simple harmonic motion

Question

At what displacement is the kinetic energy of a particle performing simple harmonic motion of amplitude 10 cm is three times it’s potential energy?

Moderate

A

10 cm
B

5 cm
C

15 cm
D

20 cm

Solution

KE=3(PE)
$w e k n o w, K i n e t i c e n e r g y K E, P o t e n t i a l e n e r g y P E a s KE= \frac{1}{2} {mω}^{2} (A^{2} {-x}^{2}) P E = \frac{1}{2} {mω}^{2} (x^{2}) b y t h e q u e s t i o n, K E = 3 P E \Rightarrow \frac{1}{2} {mω}^{2} (A^{2} {-x}^{2}) = \frac{3}{2} {mω}^{2} (x^{2}) o n s i m p l i f i c a t i o n, A^{2} {=4x}^{2} \Rightarrow x=A/2 G i v e n A = 10 c m ∴ x = \frac{10}{2} = 5cm$

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