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physics A-Level Physics
 
Solved problems for the chapter:
 

Damping

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Detailed solution steps are available at:
 
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Example 1.

A pendulum oscillates with a frequency of 1 Hz. With each oscillation, its amplitude drops by 10 %. What is its damping factor?

    
Example 2.

How do we get damped oscillation? Write an equation and draw the graph of the relationship between the displacement from the equilibrium position and time.

    
3.

A simple pendulum oscillates with an amplitude of 12 cm and a period of 0.5 s. The oscillation is damped. The damping factor is . How does the total energy of the pendulum change as it oscillates? Draw the graph for the first six oscillations.

    
4.

The amplitude of a simple pendulum is measured as a function of time with a detector. The obtained data are shown in the table below.


[s]00.30.60.91.21.51.82.12.42.73 
10- 0.7600.580- 0.4400.340- 0.26 

  • From this data, plot the graph of as a function of time .

  • Read from the graph the type of oscillation of the pendulum.

  • Calculate the angular frequency of the oscillation and the damping coefficient.

  • What is the length of the pendulum?


    
5.

The string of a simple pendulum is 1.5 m long. At the beginning, the weight is displaced by 10 cm from the equilibrium position and after six oscillations, the amplitude is equal to 5 cm.

  • What is the relationship between the amplitude and time in a damped oscillation?

  • Calculate the damping coefficient.

  • What will be the amplitude of the oscillation after 1 min?

  • Calculate the ratio between the oscillation energy after 2 oscillations and the initial energy.

    
6.

A simple pendulum with a mass oscillates with a frequency . The oscillation is damped by the coefficient , and the initial amplitude of the oscillation is .

  • Express the relationship between oscillation energy and time with only the given data.

  • What happens to the energy of the oscillation if we double the frequency?

  • In what way and by what percentage does the energy change if the frequency is five times the initial, the amplitude is one-third the initial, and the mass of the pendulum is one-fourth the initial?

    
7.

A hypnosis clock has a mass of 0.2 kg and hangs on a string with a length of 0.35 m. The hypnotist initially oscillates with the clock slowly with an amplitude of 2 cm. Then he begins a forced oscillation such that the amplitude is equal to a quarter of the length of the string. At least how many oscillations does it take for this to happen if the hypnotist adds of energy with each oscillation? Assume that we are dealing with a simple pendulum.