# SHM

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What did Galileo observe about pendulum swings?
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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## Other cards in this set

### Card 2

#### Front

What's the formula for angular frequency?

#### Back

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

### Card 3

#### Front

What do restoring forces accomplish?

### Card 4

#### Front

Acceleration is proportional to...

### Card 5

#### Front

Acceleration equals..