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

As the given equation is
`x=acos(alphat)^2`
is a cosine fucntion. Hence, it is an oscillatory motion.
Now, putting `t+T` in place of t
`x(t+T)=acos[alpha(t+T)]^(2)" "[because x(t)=acos(alphat)^2]`
`=acos [alpha^(2)t^(2)+alpha^(2)T^(2)+2alpha^(2)tT]ne x(t)`
where, T is supposed as period of the function `omega (t)`. Hence, it is not periodic.