Energy in Oscillations (Oxford AQA IGCSE Physics)

Revision Note

Energy in Oscillations

  • An oscillating object moves back and forth in a regular rhythm

  • The energy in an oscillating system is transferred back and forth between gravitational potential and kinetic energy stores

  • Examples of oscillating objects are:

    • A simple pendulum

    • A guitar string

    • A swing

    • A bungee jump

    • A mass on a spring

    • Alternating current

  • A simple pendulum consists of a mass (called a bob) on a string

  • If the bob is displaced from its equilibrium position and left to swing freely, it will oscillate

A simple pendulum

A simple pendulum for IGCSE & GCSE Physics revision notes
A simple pendulum consists of a bob on a string
  • As the pendulum oscillates, energy is transferred back and forth between the gravitational potential and kinetic stores

  • In an ideal system (where there is no air resistance) the total energy of the oscillating pendulum remains constant

  • The position at which the pendulum would hang undisturbed is called the equilibrium position

  • The pendulum is considered to have zero gravitational potential energy at the equilibrium position

  • As the pendulum is displaced from the equilibrium position, energy is transferred to its gravitational potential store

  • When the pendulum is released and begins to swing, energy is transferred from the gravitational potential store to the kinetic store

  • The pendulum has the most kinetic energy as it swings through the equilibrium position because this is when its velocity is the greatest

  • As it swings past the equilibrium position to the other side of the oscillation, energy is transferred from the kinetic store to the gravitational potential store

  • As the pendulum bob reaches its point of maximum displacement from the equilibrium position, its velocity slows to zero (at the point at which it changes direction) so there is zero energy in its kinetic store and maximum energy in its gravitational potential store

Energy changes in an oscillating object

A red horizontal line shows the total energy is constant. A parabolic U shape shows the change in the gravitational potential energy store, and an inverted U shape shows the change in the amount of energy in the kinetic store
The red line on the graph shows that the total energy in an ideal oscillating system is constant. This energy is transferred back and forth between the kinetic and gravitational potential stores throughout the oscillation

Worked Example

At a certain point in the oscillation of a simple pendulum, the ideal system has 8 J in the kinetic store and 13 J in the gravitational potential store.

Determine the total energy in the oscillating system.

Answer:

Step 1: List the known quantities

  • Kinetic energy, E subscript k space equals space 8 space straight J

  • Gravitational potential energy, E subscript p space equals space 13 space straight J

Step 2: Recall the relationship between total energy, kinetic energy, and gravitational potential energy

  • The total energy of the system remains constant

  • Energy is transferred back and forth between the kinetic and gravitational potential stores

  • Therefore:

E subscript t o t a l end subscript space equals space E subscript k space plus space E subscript p

Step 3: Determine the total energy of the system

E subscript t o t a l end subscript space equals space 8 space plus space 13

E subscript t o t a l end subscript space equals space 21 space straight J

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