Total Energy of SHM (College Board AP® Physics 1: Algebra-Based)

Total energy of SHM

Calculating total energy

• Only two types of energy store are considered in SHM systems:

  • Kinetic energies

  • Potential energies

• The total energy of the system is the sum of these energies:

• Where:

  • is the total energy of the system, measured in

  • is the total potential energy of the system, measured in

  • is the total kinetic energy of the system, measured in

• It is assumed that no work is done by resistive forces such as drag or friction

  • This means no energy enters or leaves the system

• For a system showing SHM, total energy remains constant

Different systems

• The potential energy in the system will differ for different systems

Horizontal object-spring system

• When oscillations are horizontal, the gravitational potential is unchanged

  • The only changing potential energy is the elastic potential energy of the spring

• This is a spring-object system, as only these two components need to be considered

Vertical object-spring-Earth system

• If an object-spring system is oscillating vertically, the gravitational potential energy is changing, as well as the elastic potential energy

  • The system must therefore include the Earth too, as it provides the field in which gravitational potential energy varies

• The potential energy then becomes the sum of elastic and gravitational potential energies

  • Elastic potential must be defined with displacement from the spring's natural length

  • Gravitational potential can be calculated with at any point, the total energy will remain constant