Core Practical 16: Investigating Resonance (Edexcel A Level Physics)

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Lindsay Gilmour

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Core Practical 16: Investigating Resonance

Aim of the Experiment

  • Determine the value of an unknown mass by a graphical method by using the resonant frequencies of the oscillation of known masses

Variables

  • Independent variable = mass (kg)
  • Dependent variable = time period (s)
  • Control variables:
    • The spring / oscillator

Equipment

  • Spring (standard 20-25 mm spring)
  • Slotted 100g masses and hanger
  • Retort stand and clamp
  • Digital timer
  • Unknown test mass
  • Digital scales

Method

13-7-cp16-equipment-set-up_edexcel-al-physics-rn

  1. Set up the spring with 100 g mass attached
  2. On the stand make a clear fiducial mark about 5 cm below the bottom of the spring
  3. Extend the spring so that the bottom is level with the fiducial marker, release and start timing
  4. Measure time for 10 oscillations
  5. Repeat with the same mass two more times
  6. Find the average time period of one oscillation
  7. Add 100 g and adjust the fiducial mark downwards so that it is 5 cm below the new level of the spring
  8. Repeat steps 3-7 until the total mass is 500 g
  9. Plot a graph of T2 on the y-axis against m on the x-axis 

Testing the unknown mass

  • Follow steps 2 - 6 for the test mass
  • Find the value of the time period, T and square it to find T2
  • On the graph mark a horizontal from T2 to the graph line and where they intersect, take the arrow vertically down to meet the x-axis
  • The value of m which this line coincides with is the mass of the test mass
  • Check the result using digital scales

13-7-cp16-graph-of-test-mass_edexcel-al-physics-rn

Analysis

  • Analysis for this graph is based on three equations related to simple harmonic motion;
    • Angular velocity, omega equals square root of k over m end root (equation 1)
    • Where k = spring constant (N kg−1) and m = mass (kg) 
    • Angular velocity, omega equals 2 πf  (equation 2)
    • Where f = frequency of oscillations (Hz) 
    • Frequency, f equals 1 over T (equation 3)
    • Where T = time period for one oscillation (s) 

  • Substitute equations 2 into equation 1;

2 straight pi f space equals space square root of k over m end root

  • Substitute equation 3 into equation 2

fraction numerator 2 straight pi over denominator T end fraction space equals space square root of k over m end root

  • Square both sides

fraction numerator 4 straight pi squared over denominator T squared end fraction space equals space k over m

  • Make T2 the subject

T squared equals m open parentheses fraction numerator 4 pi squared over denominator k end fraction close parentheses

  • Plot a graph of T2 on the y-axis against m on the x-axis to get a straight line through the origin with;

gradient = open parentheses fraction numerator 4 pi squared over denominator k end fraction close parentheses

Safety Considerations

  • Clamp stand to the desk for stability
  • Wear safety glasses in case the spring flies off or snaps
  • Place a cushion or catch-mat in case of falling masses

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Lindsay Gilmour

Author: Lindsay Gilmour

Expertise: Physics

Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.