# SIMPLE PENDULUM CALCULATOR

Simple pendulum calculator to find pendulum period, frequency and length in physics.

A simple pendulum motion is moving back and forth of an object suspended from the end of a massless unstretchable string with negligible friction. When the object is pulled to one side of its equilibrium position and released, it oscillates.

For small angles (the angles less than 15°) approximation, the formula of pendulum period is T = 2π (l/g)^0.5. Here l stands for pendulum length, g is acceleration of gravity and T is the period.

When the amplitude of the pendulum motion is not small, the differences from simple harmonic motion can be significant. The period can be expressed by an inﬁnite series;

$$T=2\pi \sqrt { \frac { l }{ g } } (1+\frac { { 1 }^{ 2 } }{ { 2 }^{ 2 } } \sin ^{ 2 }{ \frac { \theta }{ 2 } } +\frac { { 1 }^{ 2 }{ 3 }^{ 2 } }{ { 2 }^{ 2 }4^{ 2 } } \sin ^{ 4 }{ \frac { \theta }{ 2 } } +.....)$$

Here θ stands for maximum angular displacement.

### Simple Pendulum Calculator:

 KNOWN PARAMETERS Length [l], Gravity [g] Length [l], Period [T] Length [l], Frequency [f] Gravity [g], Period [T] Gravity [g], Frequency [f] INPUT PARAMETERS Acceleration of Gravity cm/s^2 m/s^2 m/h^2 km/h^2 in/s^2 ft/s^2 miles/h^2 Pendulum Length [l] mm m inch ft Pendulum Period [T] s Pendulum Frequency [f] Hz

Note: Use dot "." as decimal separator.

 RESULTS Acceleration of Gravity [g] Label Pendulum Length [l] Label Pendulum Period [T] s Pendulum Frequency [f] Hz

Note: Default rounding is 5 decimal places.

### Simple Pendulum Example:

Find the period and frequency of a simple pendulum 1.5 m long at a location where g is 9.8 m/s2.

Solution:

$$T=2\pi \sqrt { \frac { l }{ g } } =2\pi \sqrt { \frac { 1.5 }{ 9.8 } } =2.458\quad s$$ $$f=\frac { 1 }{ T } =\frac { 1 }{ 2.458 } =0.407\quad Hz$$