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>>Oscillations
>>Velocity and Acceleration in SHM
>> $The time period of oscillation of a S.H.$

Question

The time period of oscillation of a S.H.O. is $\frac{π}{2} s$ . Its acceleration at a phase angle $\frac{π}{3}$ rad from extreme position is $2 m / s^{2}$ , what is its velocity at a displacement equals to half of its amplitude from mean position?

A

$0.707 m / s$

B

$0.866 m / s$

C

$2 m / s$

D

$3 m / s$

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Solution

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Correct option is B)

$a = ω^{2} x$
$x = A c o s \frac{π}{3}$
$ω = \frac{2 π}{T}$
$T = \frac{π}{2}$
$ω = 4$
$2 = (4 T^{2} \times A \times \frac{1}{2})$
$A = \frac{1}{4}$
$V = ω \times (A)^{2} - x^{2}$
$x = \frac{A}{2}$
$V = ω A \times \frac{3}{2}$
$V = 0.866 m / s e c$

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