A small driven oscillator has an expected resonance between 4 Hz and 8 Hz. (a) Formulate a research question about driving frequency and steady amplitude. [2] (b) Give a reasoned hypothesis that includes resonance and damping. [3] (c) Design a method using a signal generator, low-power driver, motion sensor and computer. Include range, controls, repeats, how to avoid transient readings, graph choice and safety. [7] (d) Explain how the method could compare two damping settings. [2] Do not invent results.

Question

Accepted Answer

Vary frequency through and beyond 4–8 Hz, measure steady amplitude at fixed driving strength, and plot amplitude against frequency. The amplitude should peak near the natural frequency; increased damping should lower and broaden the peak. (a) Ask: How does driving frequency from 2 Hz to 10 Hz affect the steady displacement amplitude of this oscillator at fixed driving force and damping? (b) Predict a maximum near the natural frequency because energy transfer is most effective when drive and response remain appropriately phased. Damping removes mechanical energy and therefore limits the peak. (c) Sweep 2–10 Hz using 1 Hz steps first, then 0.2 Hz steps around the observed maximum. Keep drive amplitude, moving mass, spring, geometry, sensor position and damping setting constant. (c) At each frequency, wait a fixed number of cycles for transients to decay, record at least ten later cycles, and calculate mean half peak-to-peak displacement. Repeat after stopping and restarting the system. (c) Plot steady amplitude against frequency and show repeat spread. Stay below the apparatus displacement limit, secure masses and springs, use a low-power driver and keep sound output at a safe, non-startling level. (d) Repeat the complete randomised frequency sequence with one measured damping change while all other controls remain fixed. Compare peak frequency, maximum amplitude and width at a stated fraction of the maximum. (d) Temperature or spring fatigue can drift over time; alternating the two damping settings at selected frequencies helps distinguish damping from time-order effects.

Map resonance without risking hearing

What a complete response should do

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