Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 17, 2023

Length (L)
Mass (m)
Height (h)

What are the fundamentals of the mathematical pendulum?

To begin, let's define a (mathematical) pendulum. A pendulum is just a weight that swings freely from a rope or stick. The "mathematical" version ignores friction losses (with air or in rotation) as well as the weight of the rod or rope from which the weight is suspended.

These approximations are good enough for all but the most accurate computations, and they allow us to concentrate on the physics at hand without having to deal with the stumbling blocks that come with a real-world setup where nothing is perfect. With these estimates, we can use this simple equation to connect a pendulum's period to its length: T = 2π√(L/g)

  • Where;
  • T = period, 
  • L = rope/rod length
  • g = acceleration due to gravity (9.8 m/s2 on average on Earth's surface).

Because physicists and mathematicians frequently teach this as the most significant pendulum equation, it is commonly taught as such. If we want to know how useful a pendulum is (as a wrecking ball, for example), we can apply this equation. It doesn't tell us anything about the pendulum's energy, speed, or how any of that relates to, say, its destructive power.

Pendulum Energy — A New Way of Thinking

More information is needed to understand how a pendulum interacts with other items. We can find out by using a physical pendulum calculator or learning how to compute potential energy (energy due to height) and kinetic energy (energy of motion) and how they are related.

Using the mathematical approximation, a pendulum's energy is always constant, changing from potential to kinetic energy and vice versa. The mass of the pendulum, as well as its vertical height, are required to calculate these quantities at any moment during its movement.

The following is the equation for the energy transformation in the pendulum: E_total = E_kin + E_pot, and it may be expanded into:

E_total = m * h * g + 1/2 * m * v2

  • Where;
  • m = pendulum's mass,
  • h = weight's height, 
  • v = weight's speed of movement.

Although the total energy (E total) appears to be unknown, it may be easily estimated using only kinetic or potential energy at a place. If we take the pendulum at its highest point (h = h max), we know the speed is 0 and E total = m * h max * g.

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FAQs on the Kinetic Energy of a Pendulum Calculator

1. What is the length of a simple pendulum?

The length of a simple pendulum is defined as the distance from the point of suspension to the bob's center and is indicated by the letter "l."

2. How do you calculate a pendulum's kinetic energy?

The kinetic energy would be KE= 1/2mv^2, where m is the pendulum's mass and v is the pendulum's speed.

3. When does the kinetic energy of the pendulum increase rapidly?

When the velocity is the maximum, the kinetic energy is the highest. At the bottom of the pendulum, something happens.

4. How do you compute a pendulum's potential energy?

The gravitational potential energy of a pendulum is determined by its height above its equilibrium position, and it can be calculated using the equation U = mgh, where m is the pendulum's mass, g is the gravitational acceleration, and h is the pendulum's height above equilibrium.