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Consider a simple harmonic motion of tim...

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement of change value from half the amplitude to the amplitude.

Text Solution

Verified by Experts

The correct Answer is:
`t_2-t_1=T/4-T/12=T/6`
`y_1=r/2, y_2=r`(for the two given position)
Now `y_1=rsinomegat_1`
`rarr r/2=rsinomegat_1`
`rarr sinomegat_1=1/2`
`rarr pit_1=omega/6`
`rarr (2pi)/(Txxt_1)=pi/6`
`rarr t_1=T/12
`Again
`y_2=rsinomegat_2`
` rarr r=rsinomegat_2`
`rarr sinomegat_2=1`
`rarr omegat_0=pi/2`
`rarr (2pi(/T)t_2=pi/2`
` rarr t_2=T/4`
So, `t_2-t_1=T/4-T/12=T/6`
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