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A particle executes SHM with a time peri...

A particle executes SHM with a time period of 2s and amplitude 10 cm . Find its (i) Displacement (ii) Velocity (iii) Acceleration after 1/6 s, Starting from mean position.

Text Solution

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(i) `T= 2s , A=10cm`
Displacement , `x=A sin . (2pi)/(T)t`
`= 10 sin . (2pi)/(2) xx (1)/(6)`
`= 10 sin . (pi)/(6)`
`= 5cm`
(ii) Velocity , `v = (dx)/(dt)= A (2pi)/(T) cos. (pi)/(T)t`
` =10 xx (2pi)/(2) cos. (2pi)/(2) xx (1)/(6)`
`= 10 xx 3.14 xx (sqrt(3))/( 2)`
`= 27.16 cm//s`
(iii) Acceleration , `a= (dv)/(dt) = (4pi^(2))/( T^(2))A sin. (2pi)/(T)t`
`= ( 4 xx ( 3.14)^(2))/(4) xx 10 xx sin .(2pi)/(2) xx (1)/(6)`
` = 49.3 cm//s^(2)`
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