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.

Answer

`t_2-t_1=T/4-T/12=T/6`

Explanation

`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`