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 timing starts as object passes through midpoint)
x = Acosωt (if timing starts from when displacement is maximum)
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
