First slide

Simple harmonic motion

Question

A body of mass 40 grams executes simple harmonic motion of amplitude 2 cm. If the time period is 0.20 seconds. What would be the total mechanical energy of system?

Moderate

A

$14.8 \times 10^{- 3} J$
B

$7.9 \times 10^{- 3} J$
C

$23.7 \times 10^{- 3} J$
D

$3.9 \times 10^{- 3} J$

Solution

Total mechanical energy of the system (given m=40 g)
$E= \frac{1}{2} {mω}^{2} a^{2} = \frac{1}{2} {×40×10}^{-3} × {(\frac{2π}{T})}^{2} {({2×10}^{-2})}^{2} = \frac{1}{2} {×40×10}^{-3} {(\frac{2 \times 3.14}{0.2})}^{2} \times {({2×10}^{-2})}^{2} = 7 .9 \times 10^{- 3} J$

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