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The pendulum as a spring

The pendulum as a spring. By the end of this presentation you will be able to Use your knowledge of the mass/spring oscillator to draw an analogy with the pendulum. Derive an expression from our mass/spring analysis to predict the time period of a pendulum.

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The pendulum as a spring

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  1. The pendulum as a spring

  2. By the end of this presentation you will be able to • Use your knowledge of the mass/spring oscillator to draw an analogy with the pendulum. • Derive an expression from our mass/spring analysis to predict the time period of a pendulum. • Summarise the quantities involved in the harmonic motion of springs and pendula.

  3. It might seem odd to think of a pendulum as a spring. Does it have a “spring constant”? Why does it behave like a spring? Length L Look at these quantities carefully.. Tension T Restoring force F Displacement s Weight mg

  4. For our spring.. (see last presentation) (2 f)2 = k/m or 2 f = (k/m) So T = 1/f = 2  m/k For the pendulum, restoring force F = horizontal component of tension T F = T (s/L) But T = mg So F = mg (s/L)

  5. Remember that the spring constant is Force/displacement. So, our “pendulum spring constant” is pendulum k = mg/L Put this into our T = 2 m/k expression Where “m/k” is now m/(mg/L) or L/g so, T for a pendulum = 2 L/g and, of course, f = 1/T

  6. SUMMARY You are likely to get questions involving oscillating springs and pendulums in the exam. Remember these expressions and use them by REARRANGING to get at the quantity you want. SPRINGS 2f = k/m f = 1/T PENDULUM 2 f = L/g f = 1/T

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