Oscillations Flashcards
Define Simple Harmonic Motion
Is when an object oscillates either side on a midpoint.
What are the conditions for SHM?
- The restoring force is directly proportional to the objects displacement from midpoint.
- Restoring force is in the opposite direction to the displacement (towards the midpoint)
What is the equation for SHM?
F = -kx
F is the restoring force. x is the displacement and k is a constant. -ve sign shows acceleration will be towards the midpoint.
Simple Pendulum Dynamics
T = 2π √ L/g
Time period is independent of mass.
Mass on a spring
T =2π√ m/k
Define Resonance
Driving frequency matches the natural frequency of a system, causing the system to gain more energy, resulting in large amplitude oscillations.
Define a free oscillation
No energy is transferred to or from surroundings. Continuous exchange of KE and PE caused by restoring force.
Natural Frequency
The frequency at which an oscillating system naturally chooses to oscillate when left alone.
Forced Oscillations
External driving force causes a driving frequency, adding energy to the system whilst it oscillates. Unless natural frequency is matched, the system won’t undergo SHM and dissipate energy.
Damped Oscillations
Energy is lost in each oscillation and reduces amplitude over time.
How may a system become damped?
Energy may be dissipated through a friction force acting on the system, or plastic deformation of a ductile material - material changes shape and absorbs energy.
Define Critical Damping
Oscillator returns to equilibrium position, as quick as possible, without overshooting.
Name the effect that results in a system being driven into large amplitude oscillations, and state the condition necessary for this to happen
Resonance. System driven at its natural frequency.
Discuss how the tuned mass dampers reduce amplitude of oscillations of the bridge and why they must be very heavily damped.
The springs/dampers absorb energy from the bridge because they oscillate with the natural frequency of the bridge, so there is maximum transfer of energy. Springs must not return energy to bridge.
Explain what happens to two springs in parallel
If two springs are added in parallel the stretching
force is shared between the springs, hence the extension for a given force is half of what it would be for a single spring. So parallel combination has twice the stiffness of a single spring
