Topic 13 Flashcards
Equation: Force of simple harmonic oscillator *
F = -kx
F = force (N)
k = spring constant
x = displacement from equilibrium (m)
Equation: Acceleration of simple harmonic oscillator *
a = -ω²x
a = acceleration (ms⁻²)
ω = 2πf = angular frequency (s⁻¹)
x = displacement from equilibrium (m)
Equation: Angular frequency *
ω = 2πf = 2π / T
ω = angular frequency (s⁻¹)
f = frequency of oscillation (Hz)
T = period of oscillation (s)
Equation: Displacement of simple harmonic oscillator *
x = A cos ωt
x = displacement (m)
A = amplitude (m)
ω = angular frequency (s⁻¹)
t = time (s)
Equation: Velocity of simple harmonic oscillator *
v = -ωA sin ωt
v = velocity (ms⁻¹)
A = amplitude (m)
ω = angular frequency (s⁻¹)
t = time (s)
Equation: Acceleration of a simple harmonic oscillator
a = -ω²A cos ωt
a = acceleration (ms⁻²)
A = amplitude (m)
ω = angular frequency (s⁻¹)
t = time (s)
What are the graphs of motion of a simple harmonic oscillator?
Equation: Time period of mass-spring oscillator *
T = 2π√(m/k)
T = period (s)
m = mass (kg)
k = spring constant
Equation: Time period of a simple pendulum *
T = 2π√(l/g)
T = period (s)
l = length of string (m)
g = gravity
What is the energy transfer for a simple pendulum?
What is a feature of the energy in an undampened pendulum?
Total energy is always constant.
What is damping?
1) Frictional forces are applied to an oscillator which it has to work against, by transferring energy through heating.
2) Therefore, the total energy and amplitude both decay exponentially.
3) This means that oscillations quickly die away.
How do you draw a damped system on a graph?
- Peaks are the same distance apart.
- Envelope of peaks decay exponentially.
Definition: Free oscillation
An oscillation where there is no external energy source after its initial displacement.
Definition: Forced oscillation
An oscillation which is driven by a periodic force that supplies energy to the oscillator.
Definition: Resonance
Occurs when the forcing frequency is equal to the natural frequency, creating a very large amplitude.
What can you do when using the oscillation equations?
Ignore the sin/cos functions.
What is a feature of an object in simple harmonic motion?
- The magnitude of force acting on the object is directly proportional to the distance from equilibrium.
- The force is directed towards equilibrium.
How do you prove an object is undergoing simple harmonic motion?
- Find the resultant force acting on it.
- Show that it acts towards equilibrium and is directly proportional to the distance from equilibrium.
