1.

The displacement of a perticle varies with time as `x = 12 sin omega t - 16 sin^(2) omega t` (in cm) it is motion is `S.H.M.` then its maximum acceleration isA. `12 omega^(2)`B. `36 omega^(2)`C. `133 omega^(2)`D. `sqrt(192) omega^(2)`

Answer» Correct Answer - B
`x = 12 sin omega t - 16 sin^(3) omega t = 4(3 sin omega t - 4 sin ^(3)omega t]`
`= 4[sin 3 omega t]` (By using `sin 3 theta = 3 sin theta - 4 sin ^(3) theta`]
`:.` Maximum acceleration `A_(max) = (3omega)^(2) xx 4 = 36 omega^(2)`.


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