SHM and oscillations

Question 1

4. A student wishes to investigate whether the period of oscillation of a simple pendulum is constant for all angles of swing. Describe how the student should carry out the investigation. Include the following in your description: (5 marks)
   a. Details of how the measurements would be made
   b. How these results would be used to form a conclusion
   c. The major difficultly that is likely to be encountered and how this might be overcome.

Answer 1

• Measure angle with a protractor
• Measure the initial and subsequent amplitude with a ruler
• Stopwatch to measure the time
• Compare the time periods for different angles
• Plot period against angle graph
• Difficulty = Angle decreased during time of swing. Solution = Video the motion with on screen timer and analyse OR use data logger with motion sensor to record many swings and analyse how the period changes.

Question 2

5. Describe damping and its effects on the wave properties of the oscillator (3 marks). Also give some examples of the practical applications of damping and comment on whether the example given uses heavy or light damping (2 marks).

Answer 2

• As amplitude decreases the time period remains constant.
• The greater the degree of damping the faster the amplitude decreases
• Damping decreases the NATURAL frequency.
• Car fuel gauges – heavy damping so that the pointer does not oscillate at all and so ignores the small, transient changes in the fuel level
• Sound level meters – light damping so as to show rapid fluctuations in sound intensity.

Question 3

6. Resonance can either be useful or be a problem. Define resonance and state how the amplitude of a system under resonance changes (2 marks). Also state and explain two examples of where resonance can be useful and state and explain two examples where resonance can be a problem (4 marks).

Answer 3

• Resonance occurs when the driving frequency matches the natural frequency
• The amplitude of vibrations is then a maximum
• Useful: Microwaves – cause water molecules to resonate
• Useful: MRI – Radio waves cause nuclei to resonate
• Problem: Bridges – Wind causes bridge to resonate
• Problem: Earthquake – Ground vibrating causes buildings to resonate