17 - Oscillations Flashcards
What is displacement of an oscillation?
The distance from the equilibrium position
What is amplitude of an oscillation?
Maximum displacement from the equilibriium
What is the period of an oscillation?
The time taken to complete one full oscillation
What is the frequency of an oscillation?
The number of oscillations per unit time
What are the two key features of SHM?
Acceleration of the object is directly proportional to its displacement
Acceleration acts in the opposite direction to the displacement
a ∝ x
a = -kx
What formula defines SHM?
a = -ω²x
a = acceleration ω = angular velocity x = displacement
If you plot a graph of acceleration against displacement, what does the gradient represent?
-ω²
When is acceleration minimum in SHM?
minimum = greatest negative
When displacement is maximum
When is acceleration maximum in SHM?
When displacement is minimum
minimum = greatest negative
What two equations can we use to calculate displacement based on a sine / cosine graph?
x = Asinωt (if displacement starts from amplitude)
x = Acosωt (if displacement starts from equilibrium)
What is the equation for velocity in SHM?
V = ±ω√(A² - x²)
What is the equation for velocity when displacement = 0?
Vₘₐₓ = ωA
Because velocity is maximum when displacement = 0
At maximum amplitude, how is the energy stored?
All potential energy, either gravitational or elastic depending on the system
At equilibrium, how is the energy stored?
All kinetic energy with no potential energy
What is the equation for kinetic energy?
Eₖ = 1/2mv²
What is the equation for elastic potential energy?
Eₚ = 1/2kx²
How do you calculate the total energy at any point in SHM of a system?
Eₜ = Eₖ + Eₚ
What does it mean when an oscillation is damped?
When an external force that acts on the object has the effect of reducing the amplitude of oscillations.
What happens when an oscillation is damped?
The amplitude is reduced until the object comes to rest.
What happens to the kinetic energy of the oscillations during damping?
It is transferred to another form, usually heat.
What is a free oscillation?
When an object is displaced from its equilibrium and then allowed to oscillate without any external forces.
What is natural frequency?
The frequency of the free oscillations of an object.
What is a forced oscillation?
When an periodic driver force is applied to the object, causing it to oscillate at the frequency of the driving force, the driving frequency.
What happens if the driving frequency is the same as the natural frequency?
The object will resonate, causing the amplitude to increase dramatically.
What can happen if high amplitude oscillations due to resonance are not damped?
The system may break.
How can resonance be useful?
Musical instruments to increase volume
MRI scans
