Pendulum Oscillations Problem

In summary, the conversation discusses a problem involving a pendulum with a light rigid rod and a meter stick suspended from a pivot. The first part of the problem requires determining the period of oscillation using the parallel-axis theorem. The second part involves finding the percentage difference between the period of this compound pendulum and a simple pendulum with a length of 1.00 m. The conversation also includes discussions on finding the moment of inertia and mass of the meter stick, and using the compound pendulum equation to solve for the period. Ultimately, the problem is solved by using the moment of inertia in the compound pendulum equation and cancelling out the mass.
  • #1
GreenLantern674
27
0
[SOLVED] Pendulum Oscillations Problem

A very light rigid rod with a length of 0.500 m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation.
(a) Determine the period of oscillation. (Hint: Use the parallel-axis theorem)
(b) By what percentage does the period differ from the period of a simple pendulum 1.00 m long?

I tried solving for period by using t=2(pi) sqrt(L/g) but that didn't work. It says to use the parallel axis theorum but I don't know what to do once I find I. Also, I don't think I can solve the second part until I get the first period, but once I do that would it just be T=2(pi) sqrt(L/g) for the period of the pendulum with 1m length?
 
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  • #2
I think that the mass of the meter stick has to be given. Check for that.

Basically, you have to treat the light rod and meter scale as a compound pendulum. You have to find the MI of the rod+scale using parallel axis theorem. If you know the MI of the scale about one end, then you can find the MI about the pivot.

Read up a bit on compound pendulum or Kater's pendulum.
 
  • #3
It definitely doesn't give the mass, although I know you need it to find MOI. Does anyone know a way around this?
 
  • #4
Never mind. I figured it out. Just put I into T=2(pi) sqrt(I/mgd) and the mass cancels out.
 
  • #5
Good for you!
 

1. What is a pendulum oscillations problem?

A pendulum oscillations problem is a physics problem that involves the motion of a pendulum, which is a weight suspended from a pivot point that swings back and forth due to the force of gravity. The goal of the problem is to determine the period, frequency, and amplitude of the pendulum's motion.

2. How do you calculate the period of a pendulum oscillations problem?

The period of a pendulum oscillations problem can be calculated using the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula assumes that the amplitude of the pendulum's motion is small (less than 15 degrees).

3. What factors affect the period of a pendulum oscillations problem?

The period of a pendulum oscillations problem is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the pendulum's motion. It is also affected by air resistance, but this is usually negligible.

4. How does the amplitude affect the period of a pendulum oscillations problem?

The amplitude of a pendulum's motion does not affect the period of a pendulum oscillations problem as long as it is less than 15 degrees. This is because the period is only dependent on the length of the pendulum and the acceleration due to gravity.

5. Can a pendulum oscillations problem be used to measure the acceleration due to gravity?

Yes, a pendulum oscillations problem can be used to measure the acceleration due to gravity. By measuring the period and length of the pendulum, the acceleration due to gravity can be calculated using the formula g = 4π²(L/T²).

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