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Flip to reveal answersWhat shape are the x, v and a graphs of an SHM oscillator against time?
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All 12 Flashcards — SHM graphs, phase and timing
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Question
What shape are the x, v and a graphs of an SHM oscillator against time?
Answer
All three are **sinusoids** (smooth waves), but **shifted** in phase relative to one another.
Question
What is the phase relationship between velocity and displacement in SHM?
Answer
Velocity **leads** displacement by a **quarter-cycle (90°)** — v is biggest at the centre, zero at the ends.
Question
What is the phase relationship between acceleration and displacement in SHM?
Answer
They are **antiphase (180° apart)** — a is the mirror image of x. This is the rule **a = -ω²x**.
Question
Where is the velocity of an SHM oscillator greatest?
Answer
At the **centre** (equilibrium, x = 0). It is **zero** at the turning points (maximum displacement).
Question
Where is the acceleration of an SHM oscillator greatest?
Answer
At the **turning points** (maximum displacement). It is **zero** at the centre, because a = -ω²x.
Question
What does the minus sign in a = -ω²x mean?
Answer
The acceleration always points **back toward the equilibrium position** (a restoring acceleration), opposite to the displacement.
Question
How long does equilibrium → maximum displacement take?
Answer
**T/4** — one quarter of the period (each quarter-cycle takes the same time).
Question
How long does it take to go from one extreme to the other extreme?
Answer
**T/2** — half a period (two quarter-cycles, passing through the centre).
Question
What is the SHM defining condition (given in the data booklet)?
Answer
$a = -\omega^{2}x$ — acceleration proportional to displacement and directed back toward equilibrium.
Question
How is the period T related to angular frequency ω?
Answer
$T = \dfrac{1}{f} = \dfrac{2\pi}{\omega}$ — both given in the data booklet.
Question
Common mistake about where the speed is greatest?
Answer
Thinking it is greatest at the ends — it is greatest at the **centre** and **zero** at the ends.
Question
In one full cycle, how many equal quarter-periods are there, and how long is each?
Answer
**Four** quarter-periods, each lasting **T/4**.
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Topic 3.1 hub
Simple harmonic motion
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