Examples of Different Vibrating Systems

An object oscillates with a time period of $1.4 \text{hrs.}$ through a tunnel dug across any of the chords of earth. How many times does it pass through its mean position in $7 \text{hrs.}$?

Which one of the following is the correct value of time period of an object oscillating inside a tunnel dug across any chord of earth?

As shown in the diagram above, a tunnel is dug across a random chord of the earth. Which one of the following components of force $F$ is responsible for its oscillation?

When an object is allowed to fall freely through a tunnel passing through any chord of the earth, it

What kind of thermodynamic process is assumed when a piston oscillates in a cylinder.

Determine the time period of a body released in a tunnel dug through the diameter of the earth.

A tunnel is dug through one of the chords from earth's surface. When an object starts to fall through that tunnel, it starts to oscillate due to gravitational force. Derive the equation for time period of its oscillation. Mass of object$=m$, mass of earth$=M$, acceleration due to gravity$=g$, radius of earth$=R$.

Assume that a tunnel is dug throughout the diameter of earth as shown in the diagram.

When a person jumps from one end of the tunnel, he/she can easily come out of the other end.

As shown in the diagram, gas is filled in a cylinder up to a level $h$ in it with a piston of a cross-sectional area $A$ and mass $M$ covering it. If the piston is given a small displacement, it starts performing simple harmonic motion. Considering the initial pressure of the gas inside the cylinder to be $P$, determine the time period of oscillation of the piston.

Define S.H.M under what condition is the motion of a pendulum simple harmonic

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 .

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

A physical pendulum consists of two thin rods of equal mass, each of length $1$ meter. The rods are joined together at point $P$ as shown in the figure below. The angular frequency of the pendulum about point $P$ (which is at the center of horizontal rod) is

(Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

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 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?