In an engine,the piston undergoes vertical simple harmonic motion with an amplitude of $7\, cm$. $A$ washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston is close to ...... $Hz$.

$A$ pendulum performs $S.H.M.$ with period $\sqrt{3} \ s$ in a stationary lift. If the lift moves up with acceleration $\frac{g}{3}$,the period of the pendulum is $[g=$ acceleration due to gravity $]$. (in $s$)

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is $(g =$ acceleration due to gravity$)$

In an experiment to determine the period of a simple pendulum of length $1\, m$,it is attached to different spherical bobs of radii $r_1$ and $r_2$. The two spherical bobs have uniform mass distribution. If the relative difference in the periods is found to be $5 \times 10^{-4}$,the difference in radii,$|r_1 - r_2|$,is best given by .... $cm$.

The time period of a simple pendulum is $2 \, sec$. If its length is increased $4$ times,then its period becomes ..... $\sec$.

$A$ simple pendulum of length $1 \ m$ and having a bob of mass $100 \ g$ is suspended in a car,moving on a circular track of radius $100 \ m$ with uniform speed $10 \ m/s$. If the pendulum makes small oscillations in a radial direction about its equilibrium position,then its time period is given by $T = 2\pi / \alpha^{1/4}$. The value of $\alpha$ is (Take $g = 10 \ m/s^2$)