$A$ function is represented by the equation $y = A \cos \omega t \cos 2\omega t + A \sin \omega t \sin 2\omega t$. Then the nature of the function is:

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \text{ m}$ represents the motion of a particle executing simple harmonic motion,the amplitude and time period of motion,respectively,are

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ Knowing initial position $x_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.
Reason $(R) :$ The amplitude and phase can be expressed in terms of $x_0$ and $p_0$. In the light of the above statements,choose the correct answer from the options given below $:$

What is the angular frequency of a reference particle executing $SHM$?

Which concepts are needed for the description of a periodic motion?

Write the difference between oscillations and vibrations.