Unit-5 Topic-6 Oscillations Answers (End-of-chapter & Examzone)

Edexcel A2 Physics Questions and answers 6.1.1 Simple harmonic motion : Simple harmonic motion

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1. a) Draw three free-body diagrams showing the forces acting on the toy in fig. 6.1.1b. The diagrams should show the situations when the toy is at its equilibrium position, and above and below the equilibrium position. b) Why might this toy not follow simple harmonic motion? a) equilibrium, mg balanced with kx; above eqm, mg + air resistance > k(x-d); below eqm, mg < air resistance + k(x+d). NB the direction of air resistance depends on the exact moment chosen b) air resistance is variable 2. a) If the lantern Galileo observed in Pisa cathedral had a mass of 5 kg hanging on a chain 4.4 m long, what would its time period have been? b) What would the angular velocity be for this lantern pendulum? c) Galileo used his own heartbeat as a stopwatch when measuring the time period. How could he have reduced any experimental error in the time measurement? a) 4.2 s

b) 1.5 rad s-1

c) keep still; take measurements over a large number of swings

3. Draw sketch graphs of the following in relation to the swinging of a pendulum: a) displacement against time b) force against time c) acceleration against time d) velocity against time e) kinetic energy against time f) potential energy against time g) total energy against time. You may need to think carefully about the motion in order to work out some of these. a) As per fig 6.1.5 b) As per fig 6.1.5 acceleration graph c) As per fig 6.1.5 d) As per fig 6.1.5 e) As per fig 6.1.7 f) As per fig 6.1.7 g) As per fig 6.1.7 4. What is the angular velocity of a child’s swing which completes 42 swings every minute? 4.4 rad s-1 5. a)What is meant by simple harmonic motion? b) Calculate the length of a simple pendulum with a period of 2.0 s. The graph in fig. 6.1.4 shows the variation of displacement with time for a particle moving with simple harmonic motion. c) What is the amplitude of the oscillation? d) Estimate the speed of the particle at the point labelled Z. e) Draw a graph of the variation of velocity, v, with time for this particle over the same period of time. Add a scale to the velocity axis. a) repeating isochronous oscillations caused by a restoring force which is proportional to the displacement. b) 0.99 m c)d)e) [need to see final aw]

Edexcel A2 Physics Questions and answers 6.1.2 Simple harmonic motion : SHM mathematics

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1. A pendulum bob has a mass of 0.6 kg and a time period of 4 seconds. If it is released from an amplitude position of 5 cm, what is its kinetic energy after eight seconds? What is its maximum kinetic energy? 8 seconds: EK = zero; EKmax = 1.85 x 10-3 J 2. If no energy were lost, a bungee jumper would continue to oscillate up and down forever. Describe the energy changes the bungee jumper would undergo. Discuss kinetic energy, different types of potential energy, and the total energy. Conclude by explaining why in real life this does not happen. GPE  KE + GPE  EPE + KE + GPE  EPE  EPE + KE + GPE  KE + GPE  GPE and repeat 3. Suggest how energy might be lost from a pendulum swinging in a vacuum. Intermolecular stresses in the string cause a heating effect, slowing the bob as kinetic energy converts to heat. 4. A grandfather clock has a 2 m long pendulum to keep time. If the owner set it at noon by setting the hands and starting the pendulum from an amplitude of 10 cm, calculate the position, velocity and acceleration of the pendulum bob at 6 seconds after noon. x6 = 0.077 m; v6 = 0.14 m s-1; a6 = 0.38 m s-2

6.2.1 Simple harmonic motion : Damped and forced oscillations

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1. Give a real life example of: a) forced oscillations b) free oscillations c) damping d) resonance Students’ own answers 2. Explain why an accelerating car may go through a brief period when a part of the dashboard rattles annoyingly. At that speed, engine frequency is at a resonant/natural frequency for that part of the dashboard. 3. Describe, using scientific terminology, how the problem in question 2 could be overcome. Significant damping, perhaps by adding a foam pad, could dissipate the vibration energy. Alternatively, altering the natural frequency of the dashboard part, perhaps by taping a weight to it, would avoid the resonance occurring. This could also be achieved by never driving fast enough to cause resonance! 4. Explain the differences between overdamping, underdamping and critical damping. Underdamping reduces amplitude of oscillations a little with each cycle. Overdamping stops oscillations entirely by returning to equilibrium very slowly. Critical damping allows nearly normal oscillation speed back to the equilibrium position, where the system is stopped.

Edexcel A2 Physics Questions and answers

6.2.2 Simple harmonic motion : Resonance problems and damping solutions

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1. Explain why the Angers bridge collapsed in 1850. The driving frequency of the soldiers marching feet matched the natural frequency of the bridge. This caused resonance and the amplitude of oscillation was so great that it caused failure of the bridge structure. 2. Explain how a damper between girders in a skyscraper could reduce damage caused by an earthquake. The damper reduces oscillation amplitude, reducing stresses on the bridge girders. 3. Explain how some dance music which has an inaudible bass frequency of between 5 and 10 Hz can get clubbers moving to the music. Body cavities have resonant frequencies and there is a particularly strong one in the chest at around 7 Hz. Thus the music causes resonance of the dancer so they vibrate more than anticipated for the volume of the music. 4. If an oscillating system is made to perform forced oscillations at a frequency close to its natural frequency, then resonance occurs. Describe how you could demonstrate qualitatively the meanings of the terms in italics. Include a diagram of the apparatus you would use. Students’ own answers

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