Swinging, equilibrium, kinetic energy problem

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SUMMARY

The discussion focuses on solving a kinetic energy problem related to a swinging motion involving a girl and a swing. Given the swing's length of 1.95 m and a time period of 2.8 s, the challenge is to calculate the kinetic energy as the girl passes through the lowest point after being displaced 250 mm from equilibrium. The correct approach involves using the conservation of energy principle, specifically the equation KE = mgh, where 'h' is the height raised above the lowest point. The participant initially misapplied the kinetic energy formula but was guided to the correct method.

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  • Understanding of simple harmonic motion and oscillations
  • Familiarity with kinetic energy calculations
  • Knowledge of conservation of energy principles
  • Ability to convert units (e.g., mm to meters)
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slymme
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Homework Statement


This is a more than one part question that depends on answers from the previous parts, which I have so I will not rewrite those questions. I will write the question I am facing difficulty with:
Answers from previous parts:
Length = 1.95 m (From top of chains to center, its a swing)
Time Period = 2.8 s
15 complete oscillations of the swing took 42 s

To set her swinging, the girl and seat were displaced from equilibrium and released from rest. This initial displacement of the girl raised the center of mass of the girl and seat 250 mm above its lowest position. If the mass of the girl was 18 kg, what was her kinetic energy as she first passed through this lowest point?

Homework Equations


T = t/n
f = 1/T
Kinetic Energy (KE) = 0.5mw^2(A^2 - x^2)
where A is amplitude and x is displacement

The Attempt at a Solution


I simply subbed in the numbers into the KE equation. I think my problem has to do with the amplitude or displacement, I might have mixed them up. But I tried swapping the numbers around but to no avail. Also, I may have quite probably interpreted the question wrong and plugged in the wrong numbers into the A and x.I put L in as the A amd 250 mm (after conversion to meter) as the x. And yes, I changed w to 2pif.
Would greatly appreciate some help :)
 
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The 250 mm is a vertical displacement of the center of mass, not a horizontal displacement.

Hint: Try a conservation law approach.
 
I've solved the question already. You were right though, I used mgh. Thanks :)
 

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