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>>Class 11
>>Physics
>>Oscillations
>>Velocity and Acceleration in SHM
>> $The time period of oscillation of a part$

Question

The time period of oscillation of a particle that executes S.H.M. is $1.2 s e c$ . The time starting from extreme position, its velocity will be half of its velocity at mean position is

A

$0.1$ s

B

$0.2$ s

C

$0.4$ s

D

$0.6$ s

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Updated on : 2022-09-05

Solution

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Correct option is A)

Time is zero at extreme position
$T = 1.2 s e c$
$v = ω A^{2} - x^{2}; v_{m a x} = ω A$
$v = \frac{v _{m a x}}{2} = \frac{ω A}{2} = ω$ $A^{2} - x^{2}$
$\frac{A ^{2}}{4} = A^{2} - x^{2}; x = \frac{3}{2} A$
$x = A$ cos $ω t$
$\frac{3}{2} A = A$ cos $ω t$
$ω t = \frac{π}{6}$

$t = \frac{π}{6 \times ω}$
$t = \frac{\neq π}{6} \times \frac{1 . 2}{2 \neq π} = 0.1 s e c$

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