# Amplitude in a simple pendulum - angle or distance?

 P: 8 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)?
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 Quote by shmurr 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)?
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, $\displaystyle \ x=A\cos(\omega t)\,,\$ 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.

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.
 P: 8 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?
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P: 7,808
Amplitude in a simple pendulum - angle or distance?

 Quote by shmurr 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?
From the length of the pendulum and from the release angle (assuming zero velocity at release) you need to calculate the amplitude, A .
 P: 8 Ok that makes sense, Thanks so much SammyS... :)
 Thanks P: 5,793 You could solve this using conservation of energy. Try it.
 P: 8 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.
 Thanks P: 5,793 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.
 P: 8 Thank you voko, finally got two formulae to give the same answer. Used energy and amplitude method.

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