What is the Frequency of Small Amplitude Oscillations in an Inverted Pendulum?

In summary, a pendulum has a mass at one end, and the other end is pivoted on a frictionless pivot so that it can turn through a complete circle. The pendulum is inverted, so the mass is directly above the pivot point. The speed of the mass as it passes through the lowest point is 6.0 m/s. If the pendulum undergoes small amplitude oscillations at the bottom of the arc, the frequency of the oscillations will be .367.
  • #1
jjd101
95
0

Homework Statement


A pendulum consists of a massless rigid rod with a mass at one end. The other end is pivoted on a frictionless pivot so that it can turn through a complete circle. The pendulum is inverted, so the mass is directly above the pivot point, and then released. The speed of the mass as it passes through the lowest point is 6.0 m/s. If the pendulum undergoes small amplitude oscillations at the bottom of the arc, what will be the frequency of the oscillations?


Homework Equations


Vmax=wA
F= 1/T


The Attempt at a Solution


I attempted to use Vmax to solve for w or A but neither w or A or given so I am not sure how to work through this problem
 
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  • #2
Check in your textbook or class notes for a discussion of pendulums. What does it say about the period (or frequency) of a pendulum?
 
  • #3
w = 2(pie)f = sqroot(g/l) is the only thing i found
 
  • #4
You can use what you found but you need a bit more.

Also think about the energy change in the mass as it drops from the top to the bottom and goes from a speed of zero to 6.0 m/sec. Draw a picture and see what you can calculate from this information.
 
  • #5
i got PE at the top = mgh = 9.8m(length of string) which is equal to 1/2mv^2 = 18m therefore L= 1.84m which would give a frequency of .367 which would give a period of 2.72? correct?
 
  • #6
Be careful here. How far does the mass fall relative to the length of the pendulum. You may be right as I haven't calculated it but you didn't mention an important point in this part of the problem. You have the right idea.
 
  • #7
the mass starts off one string length above the pivot of the pendulum and ends up one string length below the pivot, how does this affect the problem?
 
  • #8
so how many string length does it fall to achieve the final velocity of 6 m/sec?
 
  • #9
jjd101 said:
the mass starts off one string length above the pivot of the pendulum and ends up one string length below the pivot...

Yes, so what is the change in height, in terms of number of string lengths?
 
  • #10
change in height is 2L, from 2L, so does this mean the PE should be double what i had since i used mgh and a height of only one L?
 
  • #11
That's what you didn't say - that your mgh is mg2L. That's correct
 
  • #12
so mgh= 9.8m(2L) which is equal to KE = 1/2m(6)^2 which gives L = .918m which gives a freq of .5199 which gives a period of 1.92s?
 
  • #13
Good job. You are using correct concepts. I haven't checked your math.
 
  • #14
Thanks!
 
  • #15
at your service :-)
 

1. What is a pendulum oscillation problem?

A pendulum oscillation problem is a type of physics problem that involves analyzing the motion of a pendulum, which is a weight suspended from a fixed point that swings back and forth due to gravity.

2. What factors affect the period of a pendulum?

The period of a pendulum, or the time it takes for one complete swing, is affected by the length of the pendulum, the mass of the weight, and the strength of gravity. It is also affected by external factors such as air resistance and the angle at which the pendulum is released.

3. How can I calculate the period of a pendulum oscillation?

The period of a pendulum 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. Alternatively, the period can be measured by timing the pendulum for multiple swings and calculating the average.

4. How does the amplitude affect a pendulum oscillation?

The amplitude, or the maximum displacement from equilibrium, does not affect the period of a pendulum oscillation. However, it does affect the velocity and kinetic energy of the pendulum, with larger amplitudes resulting in higher velocities and kinetic energy.

5. What are some real-world applications of pendulum oscillations?

Pendulum oscillations have numerous real-world applications, including timekeeping devices such as pendulum clocks and metronomes. They are also used in seismometers to measure and record earthquake activity, and in motion sensors to detect movement. Additionally, pendulum oscillations are utilized in engineering and physics experiments to study and understand various concepts and principles.

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