Amplitude in a simple pendulum - angle or distance?

In summary, amplitude in a simple pendulum can be measured as an angle or a distance, with angles being expressed in degrees or radians. The equation for this is x=Acos(ωt), with A representing the amplitude as either a distance or an angle, ω being in radians per second, and t being in seconds. When calculating the maximum velocity of a pendulum, the amplitude value should be determined using the length of the pendulum and the release angle. There is no straightforward equation to convert amplitude in terms of an angle to a distance, but it can be calculated using a right triangle formed by the equilibrium and maximum displacement positions.
  • #1
shmurr
8
0
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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  • #2
shmurr said:
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, [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:
  • #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?
 
  • #4
shmurr said:
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 .
 
  • #5
Ok that makes sense, Thanks so much SammyS... :)
 
  • #6
You could solve this using conservation of energy. Try it.
 
  • #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.
 
  • #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.
 
  • #9
Thank you voko, finally got two formulae to give the same answer. Used energy and amplitude method.
 

1. What is the definition of amplitude in a simple pendulum?

The amplitude in a simple pendulum refers to the maximum displacement of the pendulum bob from its equilibrium position.

2. Is the amplitude in a simple pendulum measured in angle or distance?

The amplitude in a simple pendulum can be measured in either angle or distance, depending on the reference point chosen.

3. How does the amplitude affect the period of a simple pendulum?

The amplitude does not affect the period of a simple pendulum, as long as the angle of displacement is within a small range (less than 15 degrees). This is known as the small-angle approximation.

4. Can the amplitude in a simple pendulum change over time?

The amplitude in a simple pendulum can change over time if there are external forces acting on the pendulum, such as air resistance or friction.

5. How is the amplitude related to the energy of a simple pendulum?

The amplitude is directly proportional to the energy of a simple pendulum. A larger amplitude means a higher potential energy and a lower kinetic energy, and vice versa.

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