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.

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)

Two simple pendulums of length $1 \mathrm{m}$ each, with bobs having masses $1 \mathrm{kg}$ and $2 \mathrm{kg}$, are hanging from the celling of an elevator. The elevator starts moving vertically downwards with acceleration $\frac{g}{10}$. Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, approximately what are the time periods of the two pendulums?

A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum is increased by 21%, the increase in the time period of the pendulum of increased length is 

In an experiment to determine the gravitational acceleration $g$ of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of $g$ at the place?

If the steel bob of a simple pendulum is replaced by a wooden bob, then its time period will

The period of oscillation of a simple pendulum of constant length at the surface of the earth is $T.$ Its time period inside mine will be-

How is the time period of simple pendulum vary with its amplitude?

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

As shown in the above figure, a cart is accelerating in the horizontal direction with a constant acceleration of $\sqrt{3}g$ and a $50 \mathrm{cm}$ long simple pendulum is suspended from its roof. Now, find the time period of small oscillations of this pendulum in second about its equilibrium position taking $g={\mathrm{\pi }}^2 \mathrm{m} {\mathrm{s}}^{-2}$:

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

Time period of a simple pendulum is $T.$ The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{\alpha }{B}T.$ The value of $\alpha$ is _______ .

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$, the time period of the pendulum will be

A vertical spring mass system has the same time period as simple pendulum undergoing small oscillations. Now, both of them are put in an elevator going downwards with an acceleration $5 \mathrm{m} {\mathrm{s}}^{-2}$. The ratio of time period of the spring mass system to the time period of the pendulum is (assume that acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

A simple pendulum is placed inside a lift which is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio $1:2$, then the acceleration of the lift is (acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

A cabin is falling freely under gravity, what is the time period of a pendulum attached to its ceiling?

The time period of a simple pendulum inside a stationary lift is $\sqrt{5} \mathrm{s}$. What will be the time period when the lift moves upwards with an acceleration $\frac{g}{4}?$