A particle executes S.H.M. starting from the mean position. Its amplitude is 'a' and its periodic time is 'T'. At a certain instant, its speed ' u ' is half that of maxim

Question

A particle executes S.H.M. starting from the mean position. Its amplitude is 'a' and its periodic time is 'T'. At a certain instant, its speed ' u ' is half that of maximum speed V max ​ . The displacement of the particle at that instant is

TestHub · Accepted Answer

The maximum speed of a particle in S.H.M. is given by $V_{max} = aω$ .

The speed $v$ at any displacement $x$ is given by $v = ω a^{2} - x^{2}$ .

Given that $v = \frac{1}{2} V_{max}$ , we have:

$ω a^{2} - x^{2} = \frac{1}{2} aω$

Squaring both sides:

$a^{2} - x^{2} = \frac{a ^{2}}{4}$

$x^{2} = a^{2} - \frac{a ^{2}}{4} = \frac{3 a ^{2}}{4}$

$x = \frac{3 a}{2}$

Answer: $\frac{3 a}{2}$

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion