Lab 2: Simple Harmonic Oscillators – Resonance & Damped Oscillations Non-Harmonic Oscillators Harmonic Oscillators Spring Constant Measuring Period for Different Amplitudes Changing Mass and Restoring Force Changing the Spring Constant Resonance and Damped Oscillations Damped Oscillations Effect of Damping Resonance Curve Buildup Time of Oscillation

Simple Harmonic Motion periodic sinusoidal motion, f and A are independent of each other. Oscillation amplitude will Damp out without a driving force due to internal friction. Build (add) up when driving frequency fD is close to resonant frequency fR. Stay small when fD is away from fR. Dm

Damped Oscillations t A You can find T (= 1/fN ) and t from this graph equilibrium You can find T (= 1/fN ) and t from this graph Natural frequency (fN) : The frequency of oscillation in the absence of an external driving force Damping time (t) : The time it takes for the amplitude to decrease by a factor of 2

Resonance Curve A plot of oscillation A versus fD Df f1 f2 Df : Width of the resonance curve at half-maximum height (FWHM)

Relationship between  and f Df : resonance width of resonance curve (continuously driven oscillation) t : damping time of damped oscillation (naturally decaying oscillation) Check if the relationship works for your experiments!

Lab 2: Sample Data – Damped Oscillation Unit B

Lab 2: Measuring TN Unit B

Lab 2: Measuring A to find  Unit B

Lab 2: Measuring  Unit B

Creating Resonance Curve Estimate the resonance frequency fR first It’s the peak frequency! Measure the oscillation amplitude A at various driving frequency fD Use the range fR ± 2 Hz Take finer steps near fR (i.e. 0.05 Hz) Note: Turn the frequency knob in only one direction (i.e. increasing f direction) Then make a resonance curve plot

Lab 2: fD = fR = 10.61 Hz Unit B

Lab 2: fD = 8.61 Hz Unit B

Lab 2: fD = 8.61 Hz Unit B

Lab 2: fD = 8.61 Hz Unit B

Lab 2: fD = 8.61 Hz Unit B

Lab 2: fD = 9.61 Hz Unit B

Lab 2: fD = 9.61 Hz Unit B

Lab 2: fD = 9.61 Hz Unit B

Lab 2: fD = 10.59 Hz Unit B

Lab 2: fD = 10.59 Hz Unit B

Lab 2: fD = 10.61 Hz Unit B

Lab 2: fD = 10.61 Hz Unit B

To determine Df easily, graph data points within ±0.5 Hz range of fR

Example Resonance Curve continue plotting all data sets

Df = f2 – f1 fR Draw a smooth curve that fits to all data points the best – don't connect points! Df f1 f2

Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Far Unit B

Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Far Unit B

Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Near Unit B

Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Near Unit B

Lab 2: Driving f = 10.61 Hz Buildup Time w/o Magnet Unit B