$A$ simple harmonic motion is represented by $F(t) = 10\sin(20t + 0.5)$. The amplitude of the $S.H.M.$ is $a = $ ....

Write the phase difference between displacement and velocity,displacement and acceleration,and velocity and acceleration for a particle executing Simple Harmonic Motion $(SHM)$.

$A$ particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small,which graph correctly depicts the position of the particle as a function of time $?$

$A$ particle is executing simple harmonic motion with time period $2 \ s$ and amplitude $1 \ cm$. If $D$ and $d$ are the total distance and displacement covered by the particle in $12.5 \ s$,then $\frac{D}{d}$ is:

$A$ particle is executing simple harmonic motion $(SHM)$ with a time period $T = 4 \ s$. At $t = 0$,the particle is at a position where its angular position is $45^\circ$ with the $x$-axis. Find the displacement equation of the particle along the $x$-axis.

Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion?
$(a)\; a=0.7 x$
$(b)\; a=-200 x^{2}$
$(c)\; a=-10 x$
$(d)\; a=100 x^{3}$