Forced Oscillations: Resonance. Forced oscillations occur when an oscillating system is driven by a periodic force that is external to the oscillating system. In such a case, the oscillator is compelled to move at the frequency νD = ωD/2π of the driving force. ... The period TN of his oscillation is equal to 1/νN.

1. FORCED OSCILLATIONS AND
RESONANCE

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3. FREE
OSCILLATION
• Definition of free oscillation: the oscillation of a body or
system with its own natural frequency and under no
external influence other than the impulse that initiated the
motion
• called also free vibration
• opposed to forced oscillation

4. FORCED
OSCILLATIONS
AND
RESONANCE
• Suppose now that instead of allowing our system to
oscillate in isolation we apply a "driving force". For
example, in the case of the (vertical) mass on a spring the
driving force might be applied by having an external force
(F) move the support of the spring up and down.
• Wd is the (angular) frequency of the driving force.
• the amplitude of these oscillations, B, depends on the
parameters of the motion,W,Wd,m,b,F
• The amplitude, B, has a maximum value when
W=Wd. This is called the resonance condition.

5. NATURAL
FREQUENCY,
DRIVEN
OSCILLATIONS,
AND
RESONANCE
 The oscillation frequency f of a system undergoing simple harmonic
motion (e.g., spring+mass or pendulum) is said to be that system’s
natural frequency.
 If we apply an external, oscillating force that serves to “drive” the
system at some driving frequency fd, then the system is able to
absorb energy via the work done by the driving force.
 The condition known as resonance is associated with the state that
maximizes the efficiency of energy transfer from the driving force to
the system. Resonance occurs when the driving frequency
matches the system’s natural frequency.

6. THEORETICALLY