Amplitude in a simple pendulum - angle or distance?

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)?

SammyS

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.

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?

SammyS

From the length of the pendulum and from the release angle (assuming zero velocity at release) you need to calculate the amplitude, A .

shmurr

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

voko

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

shmurr

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.

voko

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.

shmurr

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