VIB - Pendulums

Pendulums

A pendulum goes through periodic motion, but it does not experience Simple Harmonic Motion. However, at very small angles it can be proved that the motion of a pendulum approaches that of Simple Harmonic Motion. The period of the pendulum depends on the length of the pendulum at small angles. The mass and the angle that it travels through do not affect the period. Please watch the following presentation that will discuss the simple Pendulum.

Pendulums Practice

We will now practice solving problems using the concepts you learned in the presentation. Make sure to show all your work when solving problems. The presentation will give you time to work through the problems, find a solution, and check your work. 

Pendulums Self-Assessment

Now it's your turn. Complete the self-assessment questions to verify that you can apply the concepts dealing with simple pendulums.

  1. A pendulum bob with a mass of 15 kg is tied to a massless string that is 3.4 m long. It is pulled back 12 degrees and released.
    1. What is the maximum gravitational potential energy of the pendulum using its equilibrium position as the zero point? 
    2. What is the maximum kinetic energy of the pendulum?
    3. What is the maximum velocity of the pendulum? 
    4. What is the maximum net force applied to the pendulum? 
    5. What would be the maximum acceleration of the bob? 
    6. What is the tension on the string at equilibrium? 
    7. What is the tension on the string at maximum displacement from equilibrium?
    8. Calculate the period of the oscillation.
    9. Calculate the frequency of oscillation.
    10. Write the angular displacement of the bob as a function of time.

SOLUTIONS Links to an external site.

  1. The position of a pendulum with respect to time is given by the equation θ=9ocos⁡(0.82t) .
    1. What is the amplitude of vibration in degrees?
    2. What is the length of the pendulum?
    3. What is the frequency of oscillation?
    4. What is the period of oscillation?
    5. What would be the maximum velocity of the bob?
    6. If maximum kinetic energy is measured to be 0.75J, what is the mass of the bob?

SOLUTIONS Links to an external site.

Pendulums Practice Problems

Download Pendulums Practice Problems Links to an external site. for more practice. 

Download solutions Links to an external site. to the practice problems. 

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