Select the wrong statement about simple harmonic motion $(S.H.M.)$.

$A$ 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

Identify the function which represents a periodic motion.

Average velocity of a particle executing $SHM$ in one complete vibration is

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36\, m$ and covers $30^{\circ}$ in $0.1\, s$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoring force per unit mass when $P$ touches $M$ will be ...... $N/kg$.

For particle $P$ revolving around the centre $O$ with radius of circular path $r$ and angular velocity $\omega$,as shown in the figure,the projection of $OP$ on the $x$-axis at time $t$ is .................