Energy loss of damped oscillator

[haruspex]

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'.

 

[vel]

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

 

[haruspex]

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.

 

[vel]

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

 

[haruspex]

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.

 

[vel]

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)

 

[haruspex]

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.