Energy in simple harmonic motion

Summary and Exam Tips for Energy in Simple Harmonic Motion

Energy in simple harmonic motion is a subtopic of Oscillations, which falls under the subject Physics in the Cambridge International A Levels curriculum. In simple harmonic motion (SHM), energy continuously shifts between kinetic and potential forms. The acceleration of an oscillator is given by $a = -\omega^2 x$, where $\omega$ is the angular frequency and $x$ is the displacement. The displacement equations, $x = x_0 \sin(\omega t)$ and $x = x_0 \cos(\omega t)$, describe the position of an object in SHM. The speed of the oscillator is maximal at the equilibrium position and can be calculated using $v = v_0 \cos(\omega t)$. Graphs of SHM depict displacement, velocity, and acceleration, showing a 90° phase difference. Energy exchange in SHM involves kinetic energy peaking at zero displacement and potential energy peaking at maximum displacement. The total energy remains constant, represented by a horizontal line on energy-time graphs. The total energy of a simple harmonic system is given by $E = \frac{1}{2} m \omega^2 x_0^2$.

Exam Tips

• Understand Key Equations: Familiarize yourself with the equations for acceleration, displacement, and speed in SHM. Knowing when to use sine or cosine functions is crucial.
• Graph Interpretation: Be able to interpret and draw displacement, velocity, and acceleration graphs, noting their phase differences.
• Energy Concepts: Remember that energy in SHM is conserved. Be prepared to explain how kinetic and potential energies interchange.
• Problem-Solving: Practice calculating total energy using $E = \frac{1}{2} m \omega^2 x_0^2$ and relate it to real-world examples like pendulums or springs.
• Focus on Magnitude: In exams, focus on the magnitude of velocity and acceleration, as direction changes periodically in SHM.