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Amplitude in a simple pendulum - angle or distance?

  1. Feb 23, 2013 #1
    Is amplitude in a simple pendulum measured as an angle, theta, or as a distance? If it is an angle, is it in radians or degrees. Also, what is the equation?

    How does amplitude relate to x=Acos(ωt)?
  2. jcsd
  3. Feb 23, 2013 #2


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    Hello shmurr. Welcome to PF !

    For a true pendulum, the amplitude can be expressed as an angle and/or a distance.

    Every angle can be expressed in degrees, also in radians.

    Regarding your equation, [itex]\displaystyle \ x=A\cos(\omega t)\,,\ [/itex] it's customary for A (the amplitude) to be a distance, although it can just as well be an angle. The quantity, ω is usually radians per second, and t is in seconds, as a time, making ωt a quantity in radians.

    Added in Edit:

    The amplitude, A, in your equation, will always be in the same units as is the variable, x. Since the variable , x, usually represents a distance, the amplitude, A, (usually) also represents a distance.
    Last edited: Feb 23, 2013
  4. Feb 23, 2013 #3
    I asked regarding this question:

    Length of pendulum = 0.760 meters
    Mass of bob = 0.365 kg
    Released at an angle = 12 degrees
    Assume SHM

    What is the maximum velocity?

    My Approach:

    maximum v = ωA
    = [(g/L)^0.5]*A

    What value of A would I put in?
  5. Feb 23, 2013 #4


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    From the length of the pendulum and from the release angle (assuming zero velocity at release) you need to calculate the amplitude, A .
  6. Feb 23, 2013 #5
    Ok that makes sense, Thanks so much SammyS... :)
  7. Feb 23, 2013 #6
    You could solve this using conservation of energy. Try it.
  8. Feb 23, 2013 #7
    Well funny thing is that I tried 3 different ways and each got me a different answer :/

    Is Amplitude = Length * (θ^2) a valid equation?

    It seems like a random one the teacher threw at us without any derivation. So I'm not exactly sure how to convert θ of amplitude into distance. Any tips?

    Also, just confirming that the amplitude is the horizontal distance from the maximum points of the bob, right?

    And thanks voko, I personally like to use conservation of energy as it makes a lot more sense. And the answer made sense.
  9. Feb 23, 2013 #8
    The amplitude of an oscillation is the maximum displacement from equilibrium. Sketch the equilibrium position and the maximum displacement position. You will get a certain right triangle. Find the displacement from this.
  10. Feb 23, 2013 #9
    Thank you voko, finally got two formulae to give the same answer. Used energy and amplitude method.
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