Period of Mass-Spring System

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 Math / Science

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.

Spring Equation Calculators

• 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.