The displacement of a particle executing linear $S.H.M.$ is given by $x = 0.25 \sin(11t + 0.5) \ m$. The period of $S.H.M.$ is (take $\pi = \frac{22}{7}$):

Write the force law for $SHM$ and obtain the formula for the period of an $SHM$ particle.

The figure shows the circular motion of a particle. The radius of the circle is $B$,the period is $30 \ s$,the sense of revolution is clockwise,and the initial position at $t = 0$ is at an angle of $45^\circ$ (or $\pi/4$ radians) with the positive $y$-axis in the first quadrant. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is:

$A$ point particle of mass $0.1\, kg$ is executing $S.H.M.$ with an amplitude of $0.1\, m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \, J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^o$.

Write the difference between oscillations and vibrations.

$A$ 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