The equation of motion of a particle is x = a cos (α t)2. The motion is

Question

The equation of motion of a particle is x = a cos (α t)2. The motion is (A) periodic but not oscillatory (B) periodic and oscillatory (C) oscillatory but not periodic (D) neither periodic nor oscillatory

Tardigrade Admin · Accepted Answer

Given x = a cos(α t)2 = a cos α2 t2 As the equation of motion involves cosine function and t2 hence it is oscillatory but not periodic.

Q. The equation of motion of a particle is $x = a cos (α t)^{2}$ . The motion is

periodic but not oscillatory

periodic and oscillatory

oscillatory but not periodic

neither periodic nor oscillatory

Given $x = a cos (α t)^{2} = a cos α^{2} t^{2}$
As the equation of motion involves cosine function and
$t^{2}$ hence it is oscillatory but not periodic.

Q. The equation of motion of a particle is x=acos(αt)2. The motion is