Ch9 - Oscillations

Define periodic motion.

Periodic motion is one in which a body continually retraces its path at equal time intervals.

Define an oscillation.

An oscillation is a special periodic motion in which the oscillator moves to and fro about an equilibrium position.

Define equilibrium position.

The equilibrium position is the position where the resultant force on the body is zero.

Define restoring force.

The restoring force is a resultant force that tries to restore a body or pendulum that has been displaced fro its equilibrium position to its equilibrium position.

Define free oscillation.

A free oscillation occurs when a body oscillates with no driving and/or resistive forces acting on it.

Define amplitude.

Amplitude is the magnitude of the maximum displacement of the particle from its equilibrium position.

Define period.

Period T is the time taken for the body to complete one oscillation.

Define frequency.

Frequency f is the number of oscillations per unit time.

Define phase (angle).

The phase (angle) ϕ of an oscillation that a body is in, is the fraction of an oscillation cycle it is at relative to its starting displacement.

Define angular frequency.

Angular frequency ω is the rate of change of phase angle of the oscillation and is equal to the product of 2πf.

Define phase difference.

Phase difference Δϕ is the difference in the positions of two oscillating bodies in their cycles.

Define simple harmonic motion (S.H.M.).

Simple harmonic motion is the motion of a particle about a fixed point (equilibrium position) such that its acceleration is proportional to its displacement from the fixed point and is always directed towards the point.

State the characteristics of the motion of a particle in simple harmonic motion.

• It is symmetrical about the equilibrium position

• Its acceleration is always directed towards the equilibrium position

• Its acceleration has maximum magnitude at maximum displacement from the equilibrium position and is zero at the equilibrium position

• Its speed is a maximum at the equilibrium position and zero at maximum displacement from equilibrium position

Define damping.

Damping is the process whereby energy is removed from an oscillating system.

State the different degrees of daming.

• Light

• Critical

• Heavy

Define light damping.

Light damping occurs when the resistive force is small. This results in oscillations where the amplitude decays exponentially with time. The frequency of oscillations is slightly lower than its natural frequency.

Define critical damping.

Critical damping occurs when the system experiences a stronger resistive force than light damping which prevents the system from oscillating. The system returns to the equilibrium position in the shortest time after its initial displacement.

Define heavy damping.

Heavy damping occurs when the system experiences an even stronger resistive force than critical damping which prevents the system from oscillating. The system takes a longer time to return to its equilibrium position after its initial displacement compared to critical thinking.

Define resonance.

Resonance occurs when the frequency of the driving force is close to or at the natural frequency of the driven system. There is maximum transfer of energy from the driver and the system responds with maximum amplitude.