First slide

Simple harmonic motion

Question

The force on a body executing SHM is 2 N when the displacement is 2 cms if the amplitude of oscillations is 5 cm. What is the total energy associated with the SHM?

Moderate

A

$1.25 \times 10^{- 2} J$
B

$125 \times 10^{- 2} J$
C

$12.5 \times 10^{- 2} J$
D

$0.125 \times 10^{- 2} J$

Solution

$T o t a l E n e r g y T E o f o s c i l l a t o r i s TE= \frac{1}{2} {mω}^{2} A^{2}, k = {mω}^{2} {F=kx=mω}^{2} x {mω}^{2} =F/x s u b s t i t u t e i n T E, TE= \frac{1}{2} (\frac{F}{x}) A^{2} S u b s t i t u t e t h e g i v e n v a l u e s TE= \frac{1}{2} (\frac{2}{2 \times 10^{- 2}}) \times {(5 \times 10^{- 2})}^{2} T E = \frac{1}{2} \times \frac{1}{10^{- 2}} \times 25 \times 10^{- 4} T E =1250 \times 10^{-4} T E =0.125 or 12.5 \times 10^{- 2} J$

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