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)
The Lagrangian of a simple pendulum can be given as: [ L = T - V ] where the kinetic energy (T) is given by (\frac{1}{2} m l^2 \dot{\theta}^2) and the potential energy (V) is given by (mgl(1 - \cos(\theta))), where (m) is the mass of the pendulum bob, (l) is the length of the pendulum, (g) is the acceleration due to gravity, (\theta) is the angle of the pendulum with the vertical, and (\dot{\theta}) is the angular velocity.
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 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).
it is less ffected by air resistance
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.
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.
applications of simple pendulum
The simple pendulum can be used to determine the acceleration due to gravity.
A simple pendulum.
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.
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 affecting a simple pendulum include the length of the string, the mass of the bob, the angle of displacement from the vertical, and the acceleration due to gravity. These factors influence the period of oscillation and the frequency of the pendulum's motion.
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.