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Oscillations

Resonance in practice and determining an unknown mass

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on where resonance is useful and where it is a problem, reducing it in a structure, and the calibration graph that turns a resonant frequency into a mass.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

Which straight-line graph relates the resonant frequency of a mass-spring system to its mass, and how is an unknown mass read off it?

Evaluation

How do a stiffer spring and added mass change the resonant frequency, what is the main uncertainty in finding it, and why is the driving amplitude kept constant?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is an example of a situation in which resonance is useful?

    Model answer

    In a radio receiver, the tuning circuit is adjusted so that its natural frequency matches the frequency of the chosen station, giving a large response only to that signal.

  2. 2

    What is an example of a situation in which resonance is a problem?

    Model answer

    A bridge or tall building can be driven into large-amplitude oscillation by wind or by marching footsteps if the driving frequency matches its natural frequency.

  3. 3

    How can the unwanted effects of resonance in a structure be reduced?

    Model answer

    By adding damping, which lowers and broadens the resonance peak, or by altering the structure so that its natural frequency is well away from any likely driving frequency.

  4. 4

    How can the resonant frequencies of known masses be used to determine an unknown mass?

    Model answer

    Attach each known mass in turn to a spring driven by a vibration generator, adjust the driving frequency until the amplitude is greatest, record that resonant frequency, and then repeat the measurement with the unknown mass in place.

  5. 5

    For a mass–spring system, what straight-line graph relates the resonant frequency to the mass?

    Model answer

    Since f = (1/2π)√(k/m), a graph of 1/f² against m is a straight line through the origin with gradient 4π²/k.

  6. 6

    How is the unknown mass read off once that calibration graph has been drawn?

    Model answer

    Its resonant frequency is measured, 1/f² is calculated, and the corresponding mass is read from the straight line.

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