Simple Pendulum

Derivation of differentiat equation for simple pendulum :-

(i) In case of simple pendulum the restoring torque depends but time period doesn't depends is.

Angular frequency of simple pendulum is ${\left(\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{L}$}\right.\right)}^{1/k}$. The value of k is _____.

Motion of simple pendulum is

Time-period of simple pendulum is 

In case of simple pendulum at small angular amplitude $\mathrm{\theta }$, the value of differential equation of simple pendulum is (when $\mathrm{L}=\mathrm{length}$ of the pendulum)

What is the second's pendulum? Find its length and frequency.

Derive the expression for the time period of a pendulum of infinite length. Show that this time is finite.

What is the time period of a second pendulum?
(Write the numerical value in terms of SI unit of time).

What provides the restoring force for simple harmonic oscillations in Simple pendulum .

If the inertial mass and gravitational mass of the simple pendulum of length $l$ are not equal, then the time period of the simple pendulum is

In case of a simple pendulum, time period versus length is depicted by

When a simple pendulum is taken from equator to poles, its period

Two pendulums of lengths $100 \mathrm{cm}$ and $110.25 \mathrm{cm}$ start oscillating in phase. After how many oscillations will they again be in the same phase?

A particle is executing $\mathrm{SHM}$  with time period $T\mathit{ }$. Starting from mean position, time taken by it to complete $\frac{5}{8}$ oscillations, is

A disc of radius $R$ and mass $M$ is pivoted at the rim about an axis which is perpendicular to its plane and its set for small oscillations. If the simple pendulum has to have the same period as that of the disc, then find the value of four times the length (in meter) of the simple pendulum if $R=\frac{1}{2} m$.

A simple pendulum suspended from the roof of a lift oscillates with frequency $f$ when the lift is at rest. If the lift falls freely under gravity, its frequency of oscillation becomes:

(Write the answer in numericals)

A simple pendulum is suspended from the ceiling of a stationary lift. Its time period is measured as $\mathrm{T}$. If the lift accelerates downward, its time period will be

A simple pendulum is suspended from the ceiling of a stationary lift. Its time period is measured as $T$. If the lift accelerates upward its time period will be 

Obtain an expression for period of simple pendulum. On which factors it depends?

Show that under certain conditions, a simple pendulum performs linear $\mathrm{S}.\mathrm{H}.\mathrm{M}.$