$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

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:

Linear simple harmonic motion is a projection of uniform circular motion along any one diameter of a circle. Is there any distinction between these two?

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

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

The displacement of a particle is given at time $t$,by: $x = A \sin (-2 \omega t) + B \sin^2 \omega t$. Then,