In SHM

Oscillations - OCR A-Level Physics

In SHM, energyThe capacity to do work. Measured in joules (J). continuously interchanges 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. (KE) and potential energyEnergy stored due to position or configuration, e.g. gravitational PE (mgh) or elastic PE (½kx²). (PE).
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): KE is maximum, PE is zero (for a system where $PE = 0$ 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..).
At maximum displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). (x = $\pm$A): KE is zero, PE is maximum.
The total energyIn SHM, the sum of kinetic and potential energy, which remains constant throughout the oscillation. remains constant throughout the motion (for undamped SHM): $E_{total}$ = $\frac{1}{2}$$m\omega$^2 $A^{2}$.
KE at displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). x: KE = $\frac{1}{2}$$m\omega$^2($A^{2}$ - $x^{2}$).
PE at displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). x: PE = $\frac{1}{2}$$m\omega$^2 $x^{2}$.
On an energy-displacement graph, KE and PE are parabolas that sum to a horizontal line (constant total energy).

Common Mistake MEDIUM

Wrong: Drawing energy-displacement graphs with KE and PE as straight lines.
Right: Both KE and PE vary as the square of displacement, so they are parabolic curves. KE is an inverted parabola (maximum at $x = 0)$ and PE is an upright parabola (minimum at $x = 0)$.