The equation of motion of a particle is
`x=acos(alphat)^(2).` The motion is

Options

A. periodic but not oscillatory
B. periodic and oscillatory
C. oscillatory but not periodic
D. neither periodic nor oscillatory

Answer

C

Explanation

The equation of motion of a particle is
`x =a cos (alpha t)^(2)`
is a cosine function and `x` varies between `-a` and `+a`, the motion is oscillatory. Now checking for periodic motion, putting `t +T` in place of `t.T` is supposed as period of the function `omega(t)`.
`x(t +T) =a cos [alpha (t+T)]^(2)`
`= alpha cos [alpha^(2)t^(2) +alpha^(2)T^(2)+2alpha^(2)tT] !=x(t)`
Hence, it is not periodic.