Question

The equation of motion of a particle 𝑖𝑠 \(x=a\cos\left( \alpha t \right)^2.\) The motion is

Answer 1

As given in question, \(x=a\cos\left( \alpha t \right)^2\)
It is cosine function, means it is oscillatory function.
Then, putting \(𝑡+𝑇\) instead of \(𝑇\)
\(x\left( t+T \right)=a\cos\left[ \alpha\left( t+T \right) \right]^2\)
\(\left[ \therefore x\left( t \right)=a\cos\left( \alpha t \right)^2 \right]\)
\(a\cos\left[ \left( \alpha t \right) ^2+2\alpha\cdot \alpha tT\right]\neq x\left( t \right)\)
Where, \(𝑇\) is period of function \(𝑥(𝑡).\)
Hence, it is not periodic.
Final answer: (c)