Galileo found the time period for a pendulum swing does not rely on its size.

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What's the formula for angular frequency?

Angular frequency is equal to ω=2π/T rads s^-1

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What do restoring forces accomplish?

Restoring forces pull oscillators back to equilibrium.

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Acceleration is proportional to...

Acceleration ∞ - displacement

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Acceleration equals..

a=-ω²x

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What is the formula for displacement?

Displacement equals Acos2πft, this can be differentiated to obtain velocity and acceleration.

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How do forces in horizontal springs work?

When there is a large displacement on a spring, the force acts in the opposite direction. Velocity is largest at equilibrium and the force builds up as the weight moves to the other side.

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What is a formula for acceleration involving force, mass, and angular frequency ?

a = F/m and a= -ω²x, F=-kx where k is spring constant, so.. a=-kx/m

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Why are models for SHM inaccurate?

Modelling oscillations holds amplitude as constant initially and it increases over time.

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What's a formula for time period?

T = 2π * (m/k)^1/2

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How can mass and time period be investigated?

T^2 is proportional to mass. This can be investigated by measuring the time for 10 oscillations of four masses in series to find the time period according to mass.

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What's the formula for a restoring force on a pendulum?

When a pendulum is displaced, it experiences a restoring force x. Restoring force, F=-Tx/L. T=mg.

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What's the formula for a time period of a pendulum?

T= 2π (L/g)^1/2

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How do forced oscillations start?

Periodic driving forces cause free oscillations to oscillate at their frequency, forced oscillations.

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How does resonance occur?

Resonance occurs when natural frequency matches the driving frequency, producing large amplitude oscillations.

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What's the formula for total energy?

Energy total = Ek+Ep = 1/2kA^2 as Ep (highest)=1/2kx^2=1/2kA^2

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How does damping work?

Damping uses forces to take energy away.

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How does damping impact resonance?

Light damping causes a significant rise in amplitude during resonance, but heavy damping causes a wider peak and smaller amplitude. Amplitude against frequency graphs can be drawn.

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