17 - oscillations

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9 Terms

1
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define simple harmonic motion

An oscillation in which the acceleration of an object is directly proportional to its displacement from its equilibrium position, and is directed towards the equilibrium

2
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what is the formula for accleration for an object in simple harmonic motion

a = -ω²𝑥

ω = angular frequency

𝑥 = displacement

3
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formula for angular velocity

ω = 2πf

4
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what conclusions can we draw from an object in SHM about its acceleration and displacement?

what two conclusions can we get if we graph acceleration and displacement from SHM?

- a∝𝑥

- the negative sign means that the acceleration acts in the opposite direction to the displacement (towards the equilibrium position)

- a gradient from the graph of this will be -ω²

- the period is independent of the amplitude

<p>- a∝𝑥</p><p>- the negative sign means that the acceleration acts in the opposite direction to the displacement (towards the equilibrium position)</p><p>- a gradient from the graph of this will be -ω²</p><p>- the period is independent of the amplitude</p>
5
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what does an isochronous osciallator mean

an oscillator where the time period of oscillation is constant and does not depend on the amplitude

6
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what are two formulas to find displacement in SHM?

what is the difference between the two?

𝑥 = A sin ωt

𝑥 = A cos ωt

sine version is when oscillator begins at equilibrium

cosine version is if it begins at max amplitude position

7
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Energy in Simple Harmonic Motion

Energy is conserved between kinetic energy and potential energy.

- kinetic at max at the equilibrium point

- potential at max on amplitude where displacement is at maximum

<p>Energy is conserved between kinetic energy and potential energy.</p><p>- kinetic at max at the equilibrium point</p><p>- potential at max on amplitude where displacement is at maximum</p>
8
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damping (simple harmonic motion)

Damping is the process by which the amplitude of oscillations decreases over time due to energy loss

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Light damping

Critical damping

Heavy damping

light damping - amplitude gradually dcreases over time