$A$ particle performs $SHM$ with a period $T$ and amplitude $a.$ The mean velocity of the particle over the time interval during which it travels a distance $a/2$ from the extreme position is

The function $\sin^2(\omega t)$ represents

The displacement of a particle in $SHM$ is given by $x = 5 \sin(\pi t)$,where $x$ is in $cm$. What is the time taken by the particle to travel from the mean position to the position of maximum displacement (in $, s$)?

The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05 \cos \left( 4 \pi t + \frac{\pi}{4} \right)$. The frequency of the motion will be ..... $Hz$.

An artificial satellite is orbiting the Earth. Is its circular motion a simple harmonic motion?

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \ s$,after starting from rest,it travels a distance $a$,and in the next $\tau \ s$ it travels $2a$ in the same direction. Then: