Period of Mass-Spring System
- A mass-spring system consists of a mass attached to the end of a spring
- The equation for the restoring force (the force responsible for the SHM) is FH = - kx
- This is the same as the equation for Hooke's Law
- The time period of a mass-spring system is given by:
- Where:
- T = time period (s)
- m = mass on the end of the spring (kg)
- k = spring constant (N m-1)
- This equation applies to both horizontal and vertical mass-spring systems:
A mass-spring system can be either vertical or horizontal. The time period equation applies to both
- The equation shows that the time period and frequency, of a mass-spring system, does not depend on the force of gravity
- Therefore, the oscillations would have the same time period on Earth and the Moon
- The higher the spring constant k, the stiffer the spring and the shorter the time period of the oscillation
Worked example
Calculate the frequency of a mass of 2.0 kg attached to a spring of spring constant 0.9 N m–1 oscillating in simple harmonic motion.
Examiner Tip
Another area of physics where you may have seen the spring constant k is from Hooke's Law. Exam questions commonly merge these two topics together, so make sure you're familiar with the Hooke's Law equation too.
