A simple pendulum performs simple harmonic motion about x = 0 with an amplitude 'A' and angular frequency ω . The speed of pendulum at x = 8 A will be.

Question

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude 'A' and angular frequency ω . The speed of pendulum at x = 8 A ​ will be.

TestHub · Accepted Answer

The velocity of a particle executing simple harmonic motion at a distance $x$ from the mean position is given by $v = ω A^{2} - x^{2}$ .

Substituting $x = \frac{A}{8}$ :

$v = ω A^{2} - (\frac{A}{8})^{2}$

$v = ω A^{2} - \frac{A ^{2}}{64}$

$v = ω \frac{63 A ^{2}}{64}$

$v = \frac{63 A ω}{8}$

Answer: $\frac{63 A ω}{8}$

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