This calculator makes it easy to calculate the period of oscillation for both springs and pendulums. You can switch between the two calculators with a simple toggle at the top—choose Spring to work with the formula T = 2π√(m/k) or Pendulum to use T = 2π√(L/g). For pendulums, you can also pick preset gravity values for Earth, the Moon, Mars, or Jupiter, or enter your own custom gravity value. Just plug in your numbers, and the calculator will instantly give you the period of oscillation.
Oscillation Period Calculator
Spring (Simple Harmonic Motion)
Where:
T = Period (s)
m = Mass (kg)
k = Spring Constant (N/m)
Pendulum (Simple Harmonic Motion)
Where:
T = Period (s)
L = Pendulum Length (m)
g = Gravity (m/s²)
Spring Period Calculator
Pendulum Period Calculator
Calculation Result
Example: Grandfather Clock Pendulum
A grandfather clock uses a pendulum with a length of 0.25 meters. On Earth (g = 9.8 m/s²), the period would be:
T = 2π√(L/g) = 2π√(0.25/9.8) ≈ 1.00 seconds
Example: Car Suspension Spring
A car’s suspension spring has a spring constant of 20,000 N/m and supports 250 kg of mass. The oscillation period would be:
T = 2π√(m/k) = 2π√(250/20000) ≈ 0.70 seconds
About Oscillation Period
The period of oscillation is the time it takes for one complete cycle of motion in a system undergoing simple harmonic motion.
Spring Systems
- Mass (m): The amount of matter in the object attached to the spring (kg)
- Spring Constant (k): A measure of the spring’s stiffness (N/m)
- Period (T): Increases with larger mass, decreases with stiffer springs
Pendulum Systems
- Length (L): The distance from the pivot point to the center of mass of the pendulum (m)
- Gravity (g): The acceleration due to gravity (m/s²)
- Period (T): Increases with longer pendulums, decreases with stronger gravity
- Note: The period of a simple pendulum is independent of the mass of the bob