Energy in simple harmonic motion
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Flip to reveal answersWhat two forms of energy interchange during SHM?
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Question
What two forms of energy interchange during SHM?
Answer
**Kinetic energy** (of motion) and **potential energy** (stored, e.g. in a stretched spring). They swap back and forth as it oscillates.
Question
What happens to the total energy of an oscillation (no friction)?
Answer
It **stays constant** — KE and PE just trade places, but their sum never changes.
Question
Where in the swing is the kinetic energy greatest?
Answer
At the **centre** (equilibrium position), where the object moves **fastest**.
Question
Where in the swing is the potential energy greatest?
Answer
At the **ends** (the amplitude), where the object is **momentarily at rest**.
Question
What is the amplitude of an oscillation?
Answer
The **greatest displacement** from the centre — the turning point where the object briefly stops.
Question
Formula for the total energy of a mass-spring oscillation?
Answer
$E_{total} = \tfrac{1}{2}kA^{2}$ — set by the amplitude A. **Not** in the data booklet, so remember it.
Question
Why does E_{total} = ½kA²?
Answer
At the amplitude the object is at rest (KE = 0), so all the energy is the elastic PE stored at the biggest stretch, ½kx² with x = A.
Question
How do you find the maximum speed of an oscillator?
Answer
Set the **maximum KE equal to the total energy**: ½mv_{max}² = ½kA², then solve for v_{max}.
Question
Double the amplitude — what happens to the total energy?
Answer
It becomes **four times larger**, because E_{total} = ½kA² depends on A² (the amplitude squared).
Question
What is the kinetic energy at the centre, in terms of the total energy?
Answer
It **equals the total energy** — at the centre the PE is zero, so all the energy is kinetic.
Question
What shape is the energy-against-displacement graph for KE and PE?
Answer
**PE** is an upward parabola (min at the centre); **KE** is a downward parabola (max at the centre); their sum is a flat line.
Question
Most common SHM-energy mistake?
Answer
Thinking the speed is greatest at the ends — it is greatest at the **centre**; at the ends the object is momentarily still.
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Simple harmonic motion
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