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`T = 2 pi sqrt( m / k )`

Enter a value for all fields

The **Period of a Mass-Spring System **calculator computes the period (Τ) of a mass-spring system based on the spring constant and the mass.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**k**) Spring Constant - (
**m**) Mass of Object (not the spring)

**Period of a Spring System (Τ): **The calculator returns the period in second. However, this can be automatically converted to compatible units via the pull-down menu.

The formula for the period of a Mass-Spring system is:

`Τ = 2π sqrt(m/k)`

where:

- Τ is the period of the mass-spring system.
- k is the spring constant in newtons per meter (N/m)
- m is the mass of the object, not the spring.

The Mass-Spring System (period) equation solves for the period of an idealized Mass-Spring System. For more information and context on this equation, please see the Mass-Spring System Calculator page.

**Period of an Oscillating Spring**: This computes the period of oscillation of a spring based on the spring constant and mass.**Mass of a Spring**: This computes the mass based on the spring constant and the period of oscillation.**Angular Frequency of a Spring**: This computes the angular frequency based on the spring constant and the mass.**Spring Constant**: This computes a spring's constant based on the mass and period of oscillation.**Work done on a Spring**: This computes the work based on the spring constant and the two positions of a spring.**Hooke's Law**: This computes the force to change the length of a spring based on the spring constant and length of displacement.**Force to Fully Compress a Spring**: This computes the force required to fully compress a spring based on the spring's physical attributes including the Young's Modulus, wire diameter, length of spring, number of windings, Poisson ratio, and outer diameter of the spring.