The displacement of a particle in $SHM$ is given by $x = 5 \sin(\pi t)$,where $x$ is in $cm$. What is the time taken by the particle to travel from the mean position to the position of maximum displacement (in $, s$)?

What is a reference particle and a reference circle?

Mark the wrong statement.

Speed $v$ of a particle moving along a straight line,when it is at a distance $x$ from a fixed point on the line is given by $v^2 = 108 - 9x^2$ (all quantities in $S.I.$ units). Then:

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 ...... $N/kg$.

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