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The generalized coordinate for the pendulum is the angle of the arm off vertical, theta. Theta is 0 when the pendulum arm is down and pi when the arm is up.

M = mass of pendulum

L = length of pendulum arm

g = acceleration of gravity

\theta = angle of pendulum arm off vertical

\dot{\theta} = time derivative of \theta

What are the kinetic and potential energies?

Kinetic energy: T = (1/2)*M*(L*\dot{\theta})^2

Potential energy: V' = MLg(1-cos(\theta))

V = -MLg*cos(\theta)

--note: we can shift the potential by any constant, so lets choose to drop the MLg

The Lagrangian is L=T-V: L = (1/2)ML^2\dot{\theta}^2 + MLg*cos(\theta)

Q: Find the Lagrangian of simple pendulum?

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Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.

The motion of the simple pendulum will be in simple harmonic if it is in oscillation.

Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.

The factors that affect a simple pendulum are; length; angular displacement; and mass of the bong.

The physical parameters of a simple pendulum include (1) the length of the pendulum, (2) the mass of the pendulum bob, (3) the angular displacement through which the pendulum swings, and (4) the period of the pendulum (the time it takes for the pendulum to swing through one complete oscillation).

Related questions

Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.

A simple pendulum exhibits simple harmonic motion

The motion of the simple pendulum will be in simple harmonic if it is in oscillation.

applications of simple pendulum

The simple pendulum can be used to determine the acceleration due to gravity.

A simple pendulum has one piece that swings. A complex pendulum has at least two swinging parts, attached end to end. A simple pendulum is extremely predictable, while a complex pendulum is virtually impossible to accurately predict.

A simple pendulum.

simple pendulum center of mass and center of oscillation are at the same distance.coupled pendulum is having two bobs attached with a spring.

The factors that affect a simple pendulum are; length; angular displacement; and mass of the bong.

The physical parameters of a simple pendulum include (1) the length of the pendulum, (2) the mass of the pendulum bob, (3) the angular displacement through which the pendulum swings, and (4) the period of the pendulum (the time it takes for the pendulum to swing through one complete oscillation).

The period of a simple pendulum of length 20cm took 120 seconds to complete 40 oscillation is 0.9.