OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(f) the period of a simple harmonic oscillator is independent of its…
Full specification wording
Simple harmonic oscillations: (f) the period of a simple harmonic oscillator is independent of its amplitude (isochronous oscillator)
An isochronous oscillator has a period that does not depend on its amplitude.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 6 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
An isochronous oscillator has a period that does not depend on its amplitude. For a mass on a spring the period is T = 2π√(m/k), and for a simple pendulum T = 2π√(l/g); neither expression contains the amplitude. Increasing the amplitude increases the distance travelled and the maximum speed in such a way that the time for one complete oscillation stays the same. This holds for an ideal simple harmonic oscillator, including a pendulum swinging through a small angle. At large amplitudes a real pendulum departs from simple harmonic motion and its period begins to increase, so the small-angle condition is part of the model.
What earns the marks
- States that the period of a simple harmonic oscillator is independent of amplitude.
- Uses T = 2π√(m/k) for a mass-spring oscillator and notes that amplitude does not appear.
- Uses T = 2π√(l/g) for a simple pendulum and notes that amplitude does not appear.
- Explains that a larger amplitude gives a larger maximum speed, so the period remains unchanged.
- Recognises that the isochronous property applies to ideal simple harmonic motion and that a real pendulum needs a small amplitude.
Common mistakes and how to put them right
Claiming that a larger amplitude always gives a longer period.
Put it right: State that period is independent of amplitude for simple harmonic motion.
Assuming the isochronous property holds for any pendulum amplitude.
Put it right: Note that the small-angle approximation is required.
Thinking that amplitude affects the period through the maximum speed.
Put it right: Explain that distance and speed increase together so the period is unchanged.
Confusing period with frequency when discussing amplitude independence.
Put it right: Note that f = 1/T, so frequency is also independent of amplitude.
Exam tips
- Quote the period equation for the oscillator in the question to show amplitude is absent.
- Use the phrase isochronous oscillator when explaining amplitude independence.
- Mention the small-angle condition when discussing a pendulum, because it defines the simple harmonic model.
Try the lesson
The start of the Simple harmonic oscillations: (f) the period of a simple harmonic oscillator is independent of its amplitude (isochronous oscillator) lesson, made from checked teaching notes for this specification point.
Listen
An isochronous oscillator has a period that does not depend on its amplitude. For a mass on a spring the period is T = 2π√(m/k), and for a simple pendulum T = 2π√(l/g); neither expression contains the amplitude. Increasing the amplitude increases the distance travelled and the maximum speed in such a way that the time for one complete oscillation stays the same. This holds for an ideal simple harmonic oscillator, including a pendulum swinging through a small angle. At large amplitudes a real pendulum departs from simple harmonic motion and its period begins to increase, so the small-angle condition is part of the model. A strong answer earns marks for these points. States that the period of a simple harmonic oscillator is independent of amplitude. Uses T = 2π√(m/k) for a mass-spring oscillator and notes that amplitude does not appear. Uses T = 2π√(l/g) for a simple pendulum and notes that amplitude does not appear. Explains that a larger amplitude gives a larger maximum speed, so the period remains unchanged. A common slip: Claiming that a larger amplitude always gives a longer period. Instead, state that period is independent of amplitude for simple harmonic motion. Exam tip: Quote the period equation for the oscillator in the question to show amplitude is absent.
Key words
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Isochronous oscillator
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Period equations
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Simple harmonic motion
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Small-angle approximation
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See every definition
- Isochronous oscillator
- An oscillator whose period does not depend on its amplitude.
- Period equations
- For a mass on a spring T = 2π√(m/k), and for a simple pendulum T = 2π√(l/g); neither expression contains the amplitude.
- Simple harmonic motion
- An idealised model in which the period is independent of amplitude, including a pendulum swinging through a small angle.
- Small-angle approximation
- The condition that is part of the model, because at large amplitudes a real pendulum departs from simple harmonic motion and its period begins to increase.
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