Oscillations & Waves Damping, Forcing, Resonance.
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Transcript of Oscillations & Waves Damping, Forcing, Resonance.
Oscillations & WavesDamping, Forcing, Resonance
Damping
• So far we have assumed that wave propagation is lossless
• In reality, friction and otherresistive forces exist
• The energy of oscillationis eventually dissipatedas heat
• 3 categories of damping
Under-damping
• Small resistive forces cause a gradual, exponential drop in amplitude
• The period of oscillation increases with the degree of damping
Critical Damping
• Resistance returns the system to equilibrium as quickly as possible without oscillation
• Critical damping is a particular case of damping
Over-damping
• The resistance is so great that no oscillations occur (as in critical damping)
• The return to equilibrium is slower than in the case of critical damping
Damping Summary
Forcing
• To counteract resistive forces, one can force an oscillation
• Forcing usually involves the application of a periodic force
• The oscillator eventually adopts the forced frequency
A different kind of forcing!!
Natural Frequency, f0
• If allowed to move freely, oscillations tend to occur at a natural frequency, denoted f0
Mismatched Forcing
• What happens if the driving frequency fD is different from the natural frequency?
• Oscillations will occur at the driving frequency, but with limited amplitude
Resonance
• What happens if the driving frequency fD matches the natural frequency?
• The driving force is synchronized with the oscillation
• Amplitude is magnified with each wave cycle
Putting it All Together
• How are damping, forcing, and resonance related?
Examples
Earthquake Preparedness
• An earthquake may excite a building’s resonant frequency, with catastrophic results
Wheel Balancing
Microwave Cooking
• Multi-atomic molecules can be visualized as mass-spring systems
• Each molecule has natural frequencies• f0 for H2O is 2.45 GHz
Timekeeping
• Clocks contain small quartz crystal tuning forks which oscillate at known frequencies
• In most watches, the crystal oscillates at 32.768 kHz
Summary
• Damping– Under-damping, critical damping, over-damping
• Forcing• Natural Frequency• Mismatched Forcing• Resonance• Examples
Homework
• In Tsokos:– Ch 4.1 - #3, 6, 8, 9, 12, 15, 17, 25, 29, 31, 37– Ch 4.2 - #1, 3, 6, 7, 12, 15, 17– Ch 4.3 - #1, 4, 5, 7, 10– Ch 4.4 - #1, 4, 7