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]

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.

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]

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 .

 

[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.