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A simple pendulum performs simple harmonic motion about x = 0 with an amplitude

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be:

Options

(a) πa / T
(b) 3π²a / T
(c) πa√3 / T
(d) πa√3 / 2T

Correct Answer:

πa√3 / T

Explanation:

Speed v = ? √(a² – x²) , x = a / 2
v = ? √(a² – a² / 4) = ? √(3a² / 4) = 2π / T . a√3 / 2
πa√3 / T

AIPMT2009
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