Energy in Simple Harmonic Motion
Total energy E = m w2 A2/2 remains constant while kinetic and potential energy exchange twice per cycle.
What is Energy in Simple Harmonic Motion?
Total energy E = m w2 A2/2 remains constant while kinetic and potential energy exchange twice per cycle.
Key formula / rule: E = m w2 A2/2, independent of position.
Key points
- Compute kinetic, potential and total energy at any displacement.
- Analyse the frequency doubling of the energy terms.
Common exam trap
Assuming kinetic and potential energy vary at the same frequency as displacement.
Definitions
- Term
Energy in Simple Harmonic Motion
- Meaning
Total energy E = m w2 A2/2 remains constant while kinetic and potential energy exchange twice per cycle.
- Term
Energy in Simple Harmonic Motion — explanation
- Meaning
Total energy depends on the square of the amplitude, so doubling the amplitude quadruples the energy. Both KE and PE vary at twice the frequency of the displacement.
Learning objectives
Compute kinetic, potential and total energy at any displacement.
Analyse the frequency doubling of the energy terms.
Formulae
- Key point
E = m w2 A2/2, independent of position.
- Key point
KE is maximum at the mean position, PE at the extremes.
- Key point
KE and PE vary with frequency 2f.
Prerequisites
PHY-U4-SHM-T1-S1-C1
PHY-U1-WEP-T1-S2-C2
Common mistakes
Assuming kinetic and potential energy vary at the same frequency as displacement.
Taking total energy proportional to the amplitude rather than its square.
Keywords
Energy
Simple
Harmonic
Motion
Practice preview
What is the formula for the total mechanical energy of a particle executing Simple Harmonic Motion (SHM) with amplitude A, angular frequency w, and mass m?…
easy
At which position during Simple Harmonic Motion (SHM) is the kinetic energy maximum?…
easy
A particle of mass 0.1 kg executes SHM with an amplitude of 0.1 m and an angular frequency of 10 rad/s. What is its kinetic energy when its displacement is 0.05 m from the equilibrium position?…
medium