Further Mechanics Flashcards
Condition for SHM
If its acceleration is directly proportional to its displacement from an equilibrium position, and always in opposite direction to displacement (i.e. always pointing towards that equilibrium position).
Damped oscillations
The amplitude of the oscillation decreases over time (due to energy losses).
Underdamped (or light damping)
The amplitude of the oscillations decreases exponentially over time. Resistive force is small compared to restoring force.
Overdamped (or heavy damping)
No oscillations occur and the system slowly returns to equilibrium (following some sort of exponential). Resistive force is large compared to restoring force.
Critically damped
Similar to heavy damping in that no oscillations occur, but this time the system returns to equilibrium the fastest.
Free Oscillations
Oscillations in which no energy is lost. (An oscillation is a repeating back-and-forth motion)
Forced Oscillations
An external driving force makes an object oscillate at the frequency of the driving force.
Resonance
An system undergoing forced oscillations is said to be in resonance when it oscillates with the maximum amplitude, approximately when the driving frequency is equal to the natural frequency of the system. In this case the system absorbs maximum energy from the source of the driving force.
Three effects on the amplitude-frequency graph when you increase damping
- Peak broadens.
- Resonant frequency decreases - i.e. the peak moves left (further from the natural frequency of the object). Maximum amplitude falls along with this.
- When you reach the point of critically damped, the resonant frequency reaches 0 (only non-zero for underdamped systems).
Natural Frequency
The unforced frequency of oscillation of an object undergoing free oscillations.
Moment of Inertia
A system’s tendency to resist angular acceleration by a torque (in the same way mass is a system’s tendency to resist linear acceleration by a force).
