First slide

Simple harmonic motion

Question

A body of mass $1 kg$ is executing simple harmonic motion. Its displacement $y (cm)$ at t seconds is given by $y = 6 \sin (100 t + π / 4)$ . Its maximum kinetic energy is

Moderate

A

6 J
B

18 J
C

24 J
D

36 J

Solution

So $a = 6 cm, ω = 100 rad / \sec$
$K_{\max} = \frac{1}{2} {mω}^{2} a^{2} = \frac{1}{2} \times 1 \times {(100)}^{2} \times {(6 \times 10^{- 2})}^{2} = 18 J$

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