Oscillations Flashcards
What is resonance?
When an external force causes an object to vibrate at it’s natural frequency.
Phase
The point an oscillating mass has reached within the complete cycle of an oscillation.
Requirements of Simple Harmonic motion.
- An oscillating mass.
- An equilibrium position of this mass.
- A restoring force to return it to equilibrium.
For an object moving with SMH, when does it have max. velocity?
At it’s equilibrium position .
Angular Frequency.
ω = 2πf or 2π/T
For displacement/time graph, the equation to use when object is at equilibrium when t=0.
x = x₀ sin ωt
For displacement/time graph, the equation to use when object isn’t at equilibrium when t=0.
x = x₀ cos ωt
Equation relating displacement and acceleration.
a = −ω²x
Direction of acceleration.
Always directed towards the equilibrium point.
Equation for changing velocity.
v = v₀ cos ωt
when t=0, v is at it’s maximum value
Equation for maximum velocity.
v = ±ω √x₀²−x²
OR
v₀ = ωx₀
What is damping?
The reduction in energy or amplitude of oscillation due to force opposing motion or a resistive force.
Conditions for resonance.
There must be a system capable of oscillating freely.
For any system in resonance.
- It’s natural frequency is equal to the frequency of the driver.
- It’s amplitude is maximum
- It absorbs maximum energy from the driver.
Resonance frequency reduces as…
Damping increases.
