$A$ particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true?

The displacement of a particle along the $x$ axis is given by $x = a \sin^2 \omega t$. The motion of the particle corresponds to

Which of the following is a necessary and sufficient condition for $S.H.M.$?

The motion of a particle as per $x = A \sin \omega t + B \cos \omega t$ is :-

The figure shows the circular motion of a particle. The radius of the circle is $B$. The particle starts at $t=0$ from the positive $y$-axis and moves clockwise. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle is given by:

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 $:$