Energy loss of damped oscillator

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SUMMARY

The forum discussion centers on calculating energy loss in a damped oscillator, specifically a rock on a rope undergoing oscillation. Participants reference gravitational potential energy (PEgrav = mgh) and the relationship between vertical displacement and energy loss over multiple swings. The discussion emphasizes the importance of accurately determining vertical displacement using trigonometric functions, particularly sine and cosine, to find the distances involved in the oscillation. The final calculation for energy lost over 10.5 swings is presented as 0.7155 Joules, highlighting the need for precision in calculations.

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  • Understanding of gravitational potential energy (PEgrav = mgh)
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  • #31
vel said:
I think we posted at the same time, lmao. I have the sine equations in #28. If I did it that all correctly and my line of thought is right, it should be PEgrav = 2.66(-9.8)(.401) = -10.45
I cannot decipher those scribblings. Please take the trouble to type in your working (as specified by the forum rules). Use the labels I made for the points to represent line lengths, e.g. OP'.
 
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  • #32
haruspex said:
I cannot decipher those scribblings. Please take the trouble to type in your working (as specified by the forum rules). Use the labels I made for the points to represent line lengths, e.g. OP'.
PP': sin(11.9) = opposite (PP')/1.45 -> 1.45sin(11.9) = .298
QQ': 1.45sin(4.1) = .103
.298 + .103 = 4.01
 
  • #33
vel said:
PP': sin(11.9) = opposite (PP')/1.45 -> 1.45sin(11.9) = .298
QQ': 1.45sin(4.1) = .103
.298 + .103 = 4.01
PP' and QQ' are horizontal distances. You are trying to find the vertical distance between P and Q.
 
  • #34
haruspex said:
PP' and QQ' are horizontal distances. You are trying to find the vertical distance between P and Q.
OP': 1.45cos(11.9) = 1.42
OQ': 1.45cos(4.1) = 1.45
OP' - OQ': 1.42 - 1.45 = -.003
 
  • #35
vel said:
OP': 1.45cos(11.9) = 1.42
OQ': 1.45cos(4.1) = 1.45
OP' - OQ': 1.42 - 1.45 = -.003
Better, but that's a bit inaccurate because you are taking the difference of two numbers that are rather close together. Keep more digits through the calculation.
 
  • #36
haruspex said:
Better, but that's a bit inaccurate because you are taking the difference of two numbers that are rather close together. Keep more digits through the calculation.
So my final would be 2.66(-9.8)(-.0274) = .7155 ? (I've got about ten minutes left to put this in; working full days and needing sleep doesn't help me solve problems, lol)
 
  • #37
vel said:
So my final would be 2.66(-9.8)(-.0274) = .7155 ? (I've got about ten minutes left to put this in; working full days and needing sleep doesn't help me solve problems, lol)

Yes, that's the energy lost over 10.5 swings, but it is not clear from post #1 exactly what you are being asked for. My guess is that it's fraction of energy lost per swing, assuming that fraction is a constant.
 

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