Amplitude in a simple pendulum  angle or distance?by shmurr Tags: angles, distance, pendulum amplitude, pendulum bob 

#1
Feb2313, 12:36 AM

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)? 



#2
Feb2313, 01:05 AM

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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. 



#3
Feb2313, 01:24 AM

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? 



#4
Feb2313, 01:31 AM

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Amplitude in a simple pendulum  angle or distance? 



#5
Feb2313, 01:48 AM

P: 8

Ok that makes sense, Thanks so much SammyS... :)




#6
Feb2313, 02:16 AM

Thanks
P: 5,496

You could solve this using conservation of energy. Try it.




#7
Feb2313, 03:17 AM

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. 



#8
Feb2313, 03:47 AM

Thanks
P: 5,496

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.




#9
Feb2313, 06:40 AM

P: 8

Thank you voko, finally got two formulae to give the same answer. Used energy and amplitude method.



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