Period of Mass-Spring System (AQA A Level Physics): Revision Note

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 $F_H=-kx$

  • This is the same as the equation for Hooke's law

• The time period of a mass-spring system is given by:

$T=2\pi \sqrt{\frac{m}{k}}$

• 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:

• 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