Simple Pendulum
Calculate the period and frequency of a simple pendulum using T=2π√(L/g). Enter the pendulum length in meters to get oscillation period, frequency, and detailed physics breakdown.
About This Calculator
The Simple Pendulum Calculator computes the oscillation period and frequency of an ideal simple pendulum based on its length. A simple pendulum consists of a point mass (bob) suspended from a frictionless pivot by a massless string. This tool is essential for physics students, educators, and engineers studying harmonic motion and oscillatory systems.
The calculator uses the standard pendulum period formula T = 2π√(L/g), where L is the pendulum length in meters and g is Earth's gravitational acceleration (9.80665 m/s²). The frequency is computed as the reciprocal of the period: f = 1/T. The formula assumes small angular displacements (less than 15° from vertical), where the motion approximates simple harmonic motion. For a 1-meter pendulum, the period is approximately 2.006 seconds and the frequency is about 0.498 Hz.
Regional Notes
Worldwide: The acceleration due to gravity varies slightly by location. At sea level, g ranges from about 9.764 m/s² at the equator to 9.834 m/s² at the poles. This calculator uses the standard value of 9.80665 m/s², which corresponds to approximately 45° latitude. The variation is minimal for most educational and practical purposes.
Precision: Results are displayed to 4 decimal places for educational accuracy. For precision engineering applications, local g values should be used based on geographic coordinates and altitude.
Frequently Asked Questions
What is the formula for a simple pendulum period?
The period of a simple pendulum is given by T = 2π√(L/g), where L is the pendulum length in meters and g is the acceleration due to gravity (9.80665 m/s² on Earth). This formula assumes small angular displacements (less than 15°).
Does the mass of the bob affect the pendulum period?
No, for a simple pendulum the period is independent of the mass of the bob. The period depends only on the pendulum length and the acceleration due to gravity, as shown by the formula T = 2π√(L/g).
What is the difference between a simple pendulum and a physical pendulum?
A simple pendulum assumes a point mass on a massless string, and its period depends only on length and gravity. A physical pendulum has a distributed mass and moment of inertia, and its period depends on the mass distribution using T = 2π√(I/mgD), where I is the moment of inertia and D is the distance from pivot to center of mass.
How accurate is the small-angle approximation for pendulum calculations?
The simple pendulum formula T = 2π√(L/g) is accurate to within 1% for angles up to 15°. For larger angular displacements, the period increases slightly and a more complex formula involving elliptic integrals is required.
How does gravity affect the pendulum period on different planets?
Gravity varies significantly across celestial bodies. On the Moon (g = 1.62 m/s²), a pendulum of the same length swings about 2.5 times slower than on Earth. On Jupiter (g = 24.79 m/s²), it swings about 1.6 times faster. The formula T = 2π√(L/g) captures this relationship.
Can I use this calculator for a grandfather clock pendulum?
Yes. A grandfather clock pendulum typically has a period of 2 seconds (one second per beat), which requires a pendulum length of about 0.994 m (99.4 cm) at standard Earth gravity. Enter 0.994 m to verify the 2-second period.
What is the relationship between pendulum period and frequency?
Period and frequency are reciprocals: f = 1/T. If a pendulum has a period of 2 seconds, its frequency is 0.5 Hz (half an oscillation per second). The calculator displays both values for your convenience.
How do I measure pendulum length correctly?
The pendulum length L is measured from the pivot point (where the string is attached) to the center of mass of the bob. For a simple string and a small dense bob, this is approximately the string length plus the bob radius.