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Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
T/6
Since, the motion is a simple Harmonic.
Its equation will be given by the equation,
Now, for the first half journey,
we will get,
Φ = 0,
In initial phase,
∴
For second Journey, from A/2 to A,
Time taken from A/2 to
Now,
∴
=T/6.