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A particle is executing a simple harmonic motion. Its maximum acceleration is α and its maximum velocity is β. Then its time period of vibration will be

Asked in AIPMT 2015 · v-x and a-x relations

• (1) (β²)/α
• (2) (2πβ)/α
• (3) (β²)/(α²)
• (4) α/β

Step-by-step solution

Why the other options are wrong

• (1) (β²)/α=((Aω)²)/(Aω²)=A, which is the amplitude — a length, not a time
• (3) (β²)/(α²)=1/(ω²), a time *squared*, and it has lost the factor 2π as well
• (4) α/β=ω itself: the reciprocal of what is wanted, and again without the 2π

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