A particle performs simple harmonic motion about X=0 with an amplitude A and time period T. The speed of the particle at X=(A/2) will be

Question

A particle performs simple harmonic motion about X=0 with an amplitude A and time period T. The speed of the particle at X=(A/2) will be (A) (π A √3/T) (B) (π A/T) (C) (π A √3/2 T) (D) (3 π2 A/T)

Tardigrade Admin · Accepted Answer

Velocity of a particle executing S.H.M. is given by v=ω √a2-x2=(2 π/T) √A2-(A2/4) =(2 π/T) √(3 A2/4)=(π A √3/T)

Q. A particle performs simple harmonic motion about $X = 0$ with an amplitude $A$ and time period $T$ . The speed of the particle at $X = \frac{A}{2}$ will be

$\frac{π A 3}{T}$

$\frac{π A}{T}$

$\frac{π A 3}{2 T}$

$\frac{3 π ^{2} A}{T}$

Velocity of a particle executing S.H.M. is given by
$v = ω a^{2} - x^{2} = \frac{2 π}{T} A^{2} - \frac{A ^{2}}{4}$
$= \frac{2 π}{T} \frac{3 A ^{2}}{4} = \frac{π A 3}{T}$

Q. A particle performs simple harmonic motion about X=0 with an amplitude A and time period T. The speed of the particle at X=2A​ will be

TπA3​​

TπA​

2TπA3​​

T3π2A​