$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

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

$A$ 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 $g = 10 \ m/s^2$)

The average speed of the bob of a simple pendulum oscillating with a small amplitude $A$ and time period $T$ is

$A$ pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point,the string is cut. Which trajectory is possible for the bob afterwards?

The bob of a simple pendulum is hanging vertically down from a fixed identical bob by means of a string of length $l$. If both bobs are charged with a charge $q$ each, what is the time period of the pendulum? (Ignore the radii of the bobs.)