PHYS-302, Physics of Waves (Summer 2007)

M2 - Damped Oscillation and Force Response (Resonance)

• RLC Circuit - derived the equation of motion, found the solution and discussed the various cases (overdamped, critically damped, underdamped). Discused the exponential decay and the damped natural frequency.
• Damping in a mass-spring system - discussed the various types of friction forces that cause damping in mechanical systems. Showed that a viscous friction force (proportional to velocity) yeilds an equation of motion exactly the same as that for the RLC circuit.
• Hands-on Activity (Resonance) - students explored the response of a damped oscillating system to a driving force. Two groups looked at a series RLC circuit and the other two groups looked at an acoustic oscillator (bottle). Both groups plotted the system response as a function of frequency for at least two values of damping. Here's a spreadsheet with the student results and with Dr. Russell's summary.
• Force Response (Resonance) - after students had observed resonance, we derived the equation of motion, for a damped, forced oscillator and discussed the solution. We discussed the three frequencies (natural frequency, damped natural frequency, and driving frequency) and what role each plays in the system response to a force. We learned why a plot of the response has the shape it does, what happens when the driving frequency equals the natural frequency and how damping affects the response at resonance.

Two groups of students (one with three and one with four students) measured the AC current in a series RLC circuit driven by a sine wave function generator. The students first measured the values of the inductance, capacitance and resistanc and calculated the natural frequency of the circuit. Then they drove the circuit with a sine wave from a function generator and used a multimeter to measure the amplitude of the current in the circuit as a function of frequency. They plotted their data using a spreadsheet. Then they changed the amount of resistance in the circuit and repeated the measurement.

The other two groups measured the pressure in a bottle (acoustic resonator) driven by a loudspeaker and a sine wave function generator. They changed the frequency and used a multimeter to measure the AC output of the microphone, and plotted their data using a spreadsheet. Then they inserted a small amount of cotton into the neck of the bottle to provide damping (impeding the air flow in the neck of the bottle) and repeated the measurements.