Pendulum equation

How do you calculate the torque of a pendulum?

The torque is the length of the string L times the component of the net force that is perpendicular to the radius of the arc. The minus sign indicates the torque acts in the opposite direction of the angular displacement: τ=−L(mgsinθ);Iα=−L(mgsinθ);Id2θdt2=−L(mgsinθ);mL2d2θdt2=−L(mgsinθ);d2θdt2=−gLsinθ.

What is a mathematical pendulum?

2.1 The Mathematical Pendulum. A particle of mass m connected by a rigid, weightless rod (or a thread) of length l to a base by means of a pin joint that can oscillate and rotate in a plane we call a mathematical pendulum (Fig. where ml 2 is a mass moment of inertia with respect to the pivot point.

How do you find the angle of a pendulum?

The formula is t = 2 π √ l / g . This formula provides good values for angles up to α ≤ 5°. The larger the angle, the more inaccurate this estimation will become. From the angle, the amplitude can be calculated and from amplitude and oscillation period finally the speed at the pendulum’s center can be calculated.

What forces act on a pendulum?

There are two dominant forces acting upon a pendulum bob at all times during the course of its motion. There is the force of gravity that acts downward upon the bob. It results from the Earth’s mass attracting the mass of the bob. And there is a tension force acting upward and towards the pivot point of the pendulum.

What does a pendulum period depend on?

The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. A pendulum will have the same period regardless of its initial angle.

Which is better bar pendulum and Kater’s pendulum?

If it’s just some random bar pendulum, then a Kater’s pendulum is enormously better, because it incorporates a bunch of clever ideas to make the effective length easy to measure. A pendulum is hanging in a lift and is oscillating.

What is the function of pendulum?

Pendulum, body suspended from a fixed point so that it can swing back and forth under the influence of gravity. Pendulums are used to regulate the movement of clocks because the interval of time for each complete oscillation, called the period, is constant.

What is K in pendulum?

The motion of a simple pendulum is very close to Simple Harmonic Motion (SHM). SHM results whenever a restoring force is proportional to the displacement, a relationship often known as Hooke’s Law when applied to springs. F = -kx. Where F is the restoring force, k is the spring constant, and x is the displacement.

How do you calculate the force of a pendulum?

This force is a function of the earth’s constant acceleration due to gravity, the pendulum bob’s mass and the angle between the pendulum and the vertical. Specifically, the force equals the mass times gravity times the sine of that angle – (F = mg sinθ).

Who discovered the law of pendulum?

Galileo Galilei

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What keeps a pendulum swinging?

This is because the swinging motion of a pendulum is due to the force of gravity generated by the earth’s size. Other factors, including a pendulum’s length, can also affect its motion. A pendulum is an object hung from a fixed point that swings back and forth under the action of gravity.

Why Kater’s pendulum is called reversible pendulum?

A reversible pendulum is a special design of a normal physical pendu- lum. It is able to swing from either of two mounting points and can be set up in such a way that the period of oscillation is the same from both these points.

What is law of pendulum?

Also called pendulum law . Physics. a law, discovered by Galileo in 1602, that describes the regular, swinging motion of a pendulum by the action of gravity and acquired momentum. the theory holding that trends in culture, politics, etc., tend to swing back and forth between opposite extremes.

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