Simple pendulums and mass–spring systems

The simple pendulum

The simple pendulum

t the only factors that affect the time period of the pendulum are the length of the pendulum and the gravity (gravitational force)

Small angle approximation

Using the sin function for these small angles barely changes the value at all. sinθ≈θ. In the context of SHM, the equations only work when angles are small (smaller than about 10°).

Equation for the time period of a pendulum

T=2π√(l/g)

Factors that affect time period

mass & spring constant

Factors that do not affect time period

amplitude & gravity

Equation for the time period of a mass–spring system

T=2π√(m/k)

Energy of SHM

When the pendulum is at the peak of its path (maximum displacement), all of its energy is gravitational potential energy. When the pendulum is at the equilibrium position, all of this energy has been transferred to kinetic energy.

Horizontal mass-spring systems

the potential energy is elastic potential energy, but the same transfer to kinetic energy occurs.

Vertical mass-spring systems

the potential energy is gravitational potential energy and elastic potential energy at the top, and elastic potential energy at the bottom. But the general principle still applies.

energy transfers in SHM