Simple Pendulum Calculator
Welcome to our simple pendulum calculator, where you can easily calculate the period of a pendulum and its frequency from its length. You've come to the right place if you want to learn more about a simple pendulum. We shall discuss some fundamentals of a simple pendulum here, including:
- What is a simple pendulum?
- How to find its frequency and period using the simple pendulum equation?
- How to find the length of the pendulum?
If you're interested in calculating the maximum speed, height, or kinetic kinetic energy of a pendulum calculator.
available in a pendulum setup, head to ourHow to use this simple pendulum calculator?
This simple pendulum calculator uses the simple pendulum equation to find the pendulum's period and frequency from its length.
- Enter the pendulum's length, and this simple pendulum calculator will determine the pendulum's period and frequency, using a period of a pendulum equation.
- Enter its frequency or period, and the calculator will find the pendulum's length using the pendulum length formula.
- The gravitational acceleration constant is set at . You can change it to a custom value if you wish.
What is a simple pendulum?
A pendulum is a mass suspended from a pivot about which it can swing freely. To classify a pendulum as a simple pendulum (or simple gravity pendulum), it must satisfy these conditions:
- The pivot must be frictionless. Air resistance must be negligible.
- The string or rod used to suspend the mass must be weightless.
Frequency and period of a pendulum
For a simple pendulum with small amplitudes such that , the period of the pendulum is independent of the mass and the amplitude. In such cases, the formula for a period of oscillation is given by:
Where:
- is the pendulum's period;
- is the pendulum's length (length of the string suspending the pendulum mass);
- is the gravitational acceleration, equal to ; and
- is the amplitude of the pendulum swing.
We can use this formula for the period of a pendulum to calculate its frequency:
Here, is the frequency of the pendulum.
For amplitudes greater than , the pendulum's period also depends on the moment of inertia of the suspended mass. In such cases, the period of a pendulum formula is given by:
Where:
- is the moment of inertia about the pivot;
- is the suspended mass; and
- is the distance from the pivot to the center of mass.
Our calculator does not perform this calculation, but we have the perfect tool for this scenario: physical pendulum calculator.
Length of a pendulum formula
We can find the length of the simple pendulum by rearranging the formula of a period of oscillation:
If you're now familiar with simple pendulum, why don't you try other calculators explaining fundamental problems of physics? Visit our trajectory calculator to learn the vertical distance formula of a thrown object or its angle of trajectory.