Energy in simple harmonic motion — common mistakes

Remember that total energy is constant in ideal SHM. If you know the amplitude, you can calculate the total energy, which simplifies finding KE or PE at any point!

Resonance is often misunderstood! Remember it's about efficient energy transfer, not just any large amplitude. Damping always works against resonance, reducing its peak effect.

In an ideal Simple Harmonic Motion system, there are no non-conservative forces like friction or air resistance to remove energy. Therefore, energy is only transformed between kinetic and potential forms, ensuring the total mechanical energy remains conserved.

Think of a spring: when it's most stretched or compressed (max displacement, $x_0$), it holds the most potential to do work (max PE). At these points, it momentarily stops, so kinetic energy is zero. Conversely, at the equilibrium position ($x=0$), the spring is relaxed, so PE is zero, and the object is moving fastest (max KE).

Damping and resonance are opposing forces in an oscillating system. Resonance causes an amplitude increase by adding energy, while damping reduces amplitude by removing energy. Higher damping levels will significantly reduce the peak amplitude achieved at resonance and make the resonance curve broader.