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physics A-Level Physics
 
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Angular Frequency and Phase Difference

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Detailed solution steps are available at:
 
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Example 1.

A pendulum oscillates sinusoidally. The deviation from the equilibrium position y(t) is given by the equation:




What is the amplitude of the oscillation, the oscillation period, and the maximum speed of this oscillation?

    
Example 2.

A pendulum oscillates harmonically at an angular velocity of . The maximum speed of the pendulum is 0.8 m/s. What is the maximum displacement of the pendulum from the equilibrium position? What is the displacement in time of 0.1 s?

    
3.

A pendulum is set into oscillation and a timer is turned on. After the time 9 s, we record 19 complete oscillations.

  • What is the frequency at which the pendulum oscillates?

  • How long does it take the pendulum to swing from one extreme position to the other?

  • What is the angular speed of the spendulum?

    
4.

The graph of the relationship between the deviation from the equilibrium position and the angle for two pendulums is given below.

  • Describe the oscillations of the two pendulums.

  • At what angle will the instantaneous displacement from the equilibrium position be the same for both pendulums?

  • What will be the deviation from the equilibrium position if the amplitude of oscillation for both pendulums is 4 cm?


    
5.

A pendulum oscillates harmonically so that it passes through the equilibrium position in time . The maximum oscillation speed is 18 cm/s and the maximum acceleration is . Calculate the speed and acceleration of the pendulum when it is displaced from the equilibrium position by half the amplitude.