Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?

The radius of the circle,the period of revolution,the initial position,and the sense of revolution are indicated in the figure. The $y$-projection of the radius vector of the rotating particle $P$ is:

$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic.
$Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).

The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...

$A$ particle is performing $SHM$ according to the equation $x = (3\, cm) \sin \left( \frac{2\pi t}{18} + \frac{\pi}{6} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$.

The equation of motion of a particle is $\frac{d^2y}{dt^2} + Ky = 0$,where $K$ is a positive constant. The time period of the motion is given by