3.6.1.2
Energy in SHM: kinetic and potential swap but total stays constant
Simple Harmonic Motion — AQA A-Level Physics
- SHM involves a continuous interchange between kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. and potential energyThe capacity to do work. Measured in joules (J)..
- For a pendulum: interchange is between kinetic and gravitational potential energyThe energy an object possesses due to its position in a gravitational fieldA region of space in which a mass experiences a gravitational force...
- For a mass-spring: interchange is between kinetic and elastic potential energyThe energy stored in a stretched or compressed spring (or other elastic object)..
- Total energy $E = E_K + E_P remains constant throughout (no dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance.)$.
Energy at key positions
- At equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. (x = 0): kinetic energyThe energy an object possesses due to its motion. is maximum, potential energy is zero.
- At amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (x = A): kinetic energyThe energy an object possesses due to its motion. is zero, potential energy is maximum.
- $E_K = 1/2\;\text{m}v^2 and E_P = 1/2 kx^2 (for spring systems).$
Energy-displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). graph
- Potential energy: U-shaped curve, zero at x = 0, maximum at $x = +/-A$.
- Kinetic energy: inverted-U curve, maximum at x = 0, zero at $x = +/-A$.
- Total energy: horizontal straight line above both curves.
- Energy is always positive. Any graph showing negative energy values is wrong.
Examiner Tips and Tricks
- You may need to draw these graphs.
- Use a ruler for the total energy line.
- Make the KE and PE curves smooth and symmetrical.
- They should cross at $x = +/-A/\sqrt{2}$.