A particle is performing S.H.M. about its mean position with an amplitude 'a' and periodic time ' T '. The speed of the particle when. its displacement from mean position' is

Question

A particle is performing S.H.M. about its mean position with an amplitude 'a' and periodic time ' T '. The speed of the particle when. its displacement from mean position' is 3 a ​ will be

TestHub · Accepted Answer

The velocity of a particle performing S.H.M. at a displacement $x$ from the mean position is given by:

$v = ω a^{2} - x^{2}$

Given $x = \frac{a}{3}$ and $ω = \frac{2 π}{T}$ , substituting these values:

$v = \frac{2 π}{T} a^{2} - (\frac{a}{3})^{2}$

$v = \frac{2 π}{T} a^{2} - \frac{a ^{2}}{9}$

$v = \frac{2 π}{T} \frac{8 a ^{2}}{9}$

$v = \frac{2 π}{T} (\frac{2 2 a}{3})$

$v = \frac{4 2 πa}{3 T}$

Answer: $\frac{4 2 π a}{3 T}$

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion