The displacement of a particle is represented by the equation y= sin^(3) omega t. The motion is………..

The displacement of a particle is represented by the equation y= sin^(

1.	The displacement of a particle is represented by the equation y= sin^(3) omega t. The motion is………..
Answer» non-periodic periodic but not simple harmonic simple harmonic with period `(2pi)/(omega)` simple harmonic with period `(pi)/(omega)` Solution :Displacement of particle `y= SIN^(3) omega t` `= (3sin omega t-4SIN 3 omega t)/(4)""[THEREFORE sin 3theta= 3sin THETA- 4sin^(3)theta]` `therefore V= (dy)/(dt)= (d)/(dt)[(3sin omega t-4sin 3omega t)/(4)]` `therefore 4v= 3omega cos omega t -4xx3 omega cos 3 omega t` `therefore 4v= 3omega cos omega t- 12omega cos 3 omega t` `therefore 4(dv)/(dt)= (d)/(dt) [3omega cos omega t- 12omega cos 3omega t]` `therefore 4a= -3omega^(2)sin omega t+ 36 omega^(2)sin 3 omega t` `therefore a= -(3omega^(2)sin omega t- 36 omega^(2)sin 3 omega t)/(4)` `= -omega^(2) ((3sin omega t+ 36 sin 3 omega t))/(4)` `therefore " It is not " a propto -omega^(2)y` Hence, motion is not SHM. As the expression is involvingsine function, hence it will be periodic.