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physics A-Level Physics
 
Solved problems for the chapter:
 

Resonance

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Pendulums
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:resonance/4391/


Example 1.

A body with a mass of 0.5 kg hangs on a 1 m-long rope attached to the ceiling. Draw a sketch with all the relevant quantities.

  • Calculate the oscillation period of this pendulum.

  • How does the oscillation period of the pendulum change and by what percentage if the length is cut into half?

  • How would the oscillation period of the pendulum change if the body is doubled?

  • What are the maximum speed and acceleration of the pendulum with half of the length if the body is swung with an amplitude of 5 cm?

  • At what frequency should we force this half-length pendulum to oscillate in order for resonance to occur?

    
Example 2.

The resonance curve of a simple pendulum is shown below:




  • What does the resonance curve show and what does the amplitude reached by the pendulum in resonance depend on?

  • Determine the oscillation period of the pendulum.

  • Determine the length of the pendulum.

  • What would the forcing frequency have to be for resonance to occur if the length of the pendulum were halved?

    
3.

A spring pendulum with a mass of 0.9 kg oscillates at an amplitude of 7 cm and makes 20 oscillations in 15 seconds.

  • What is the force constant of the spring?

  • What is the maximum speed of the pendulum?

  • Now we start to force this pendulum to oscillate. Is a forcing frequency of 1.0 Hz good enough to achieve resonance? If not, how would you have to change the mass to achieve resonance?