For a particle performing linear $S.H.M.$,its average speed over one oscillation is ($A=$ amplitude of $S.H.M.$,$n=$ frequency of oscillation) (in $nA$)

The equation of a particle executing $SHM$ is given by $x = 3 \cos(\frac{\pi}{2}t)$ cm,where $t$ is in seconds. The distance travelled by the particle in the first $8.5$ seconds is:

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 $:$

Which of the following expressions represent simple harmonic motion?

What are called normal modes of oscillation of a system?

$A$ particle executing simple harmonic motion along the $Y$-axis has its motion described by the equation $y = A \sin(\omega t) + B$. The amplitude of the simple harmonic motion is