First slide

Simple hormonic motion

Question

The kinetic energy of a particle, executing S.H.M. is 16 J, when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillations is

Moderate

A

$π / 2 \sec$
B

$2 πsec$
C

$20 π sec$
D

$(π / 5) \sec$

Solution

Here
$\frac{1}{2} {MA}^{2} ω^{2} = 16 joule Given that A = 25 cm = 0 \cdot 25 m M = 5.12 kg and ω = 2 π / T ∴ \frac{1}{2} \times (5 \cdot 12) (0 \cdot 25)^{2} (4 π^{2} / T^{2}) = 16 Solving, weget T = π / 5 \sec .$

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