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Question

A particle performing simple harmonic motion undergoes displacement of A2 (where A is the amplitude of simple harmonic motion) during first second. At t=0, the particle may be at the extreme position or mean position. The period of the simple harmonic motion can be

A
6 s
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B
2.4 s
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C
12 s
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D
1.2 s
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Solution

The correct option is C 12 s
At t=0, when particle is at extreme position, the situation is as shown in Fig. 1

From the figure, cosθ=A2A=12
θ=π3π3=ωt=2πT×1T=6 s

At t=0, when particle is at mean position, the situation is as shown in Fig. 2

θ=ωt
From the figure, sinθ=A2A
θ=π6,
π6=ωt=2πT×1T=12 s

Why this question ?

Key Concept: Simple harmonic motion can be visualized as the projection of uniform circular motion onto one axis.

Tip: The phase angle ωt in SHM corresponds to the real angle ωt through which the ball has moved in circular motion.

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