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Which of the following functions represent SHM : sin omega t+ 2 cos omega t |
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Answer» Solution :(a) ` X = A sin omega t + B cos 2 omega t` `(dx)/(dt) = A omega cos omega t - B (2 omega) sin 2 omega t ` ` (d^2 x)/(dt^2) = - omega^2 (A sin omega t + 4B cos 2 omega t )` `(d^2 x)/(dt^2) ne - omega^2 x ` . This differential equation is not LIKE the differential equation of a SH M. There for `x = A sin omega t+ B cos 2 omega t ` does not REPRESENT SHM (b) ` x = AE^(i omega t) ` `(dx)/(dt) = A omega e^(i omega t)` `(d^2 x)/(dt^2) = - A omega^2 e^(i omega t) = - omega^2 x ` This differential equation is like the differential equation of SHM. Therefore, `x = A e^(i omega t)`represents SHM. (iv) `x = A ln omega t` ` (dx)/(dt) = ( (A)/(omega t) ) omega = A/t` `(d^2x)/(dt^2) = ( (A)/(omega t) ) omega = A/t` `(d^2 x)/(dt^2) = - (A)/(t^2) rArr (d^2x)/(dt^2) ne - omega^2 x ` This differential equation is not like the differential equation of a SHM. Therefore, x = `A ln omega t `does not represent SHM |
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