The differentiation of energy by time
Fixed Aging Spring.pdf click here!
The differentiation of energy by time
Suppose we can press a spring inward taking no time to do this and then hold the spring fixed
Dear Scientist,
The integration of dE = F dx is solved for the equations 1 and 2. After that we differentiate the result by dt. The equation 1 is independent of t , so that is zero. But equation 2 is dependent on t , so that results to equation 5.
Equation 7 does the differentiation by dt first and then integrates the right side to come to the same result. That is equation 5.
Is the picture correct for math?
The equation 1 is a spring with no aging or degrading. The spring is fixed. There is no movement. The dx/dt is zero. This is the equation 9. The equation 2 is a spring with aging, degrading per second. The spring is fixed. There is no movement. So c0 is Newton/meter and c1 is Newton/(meter second). The value of c1 is negative. The aging, degrading spring is losing (c1 times x ) Newton per second. The meaning of dE = F dx is of course the energy inside the spring. The dE/dt is the energy lost per second in the aging , degrading spring.
Is the math correct for physics?
The equation 7 is not accepted in physics. In physics the red box is not accepted.
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Dear Professor XX,
I am having a problem with calculating the energy loss per second in a fixed, degrading , aging spring.
The red box in the picture below is the problem.
This mathematical term does not exist in physics right now.
Suppose we found that the force out of the spring F = (c0 + c1 t) x.
Lets calculate energy per second according to:
Energy is dE = Fdx
and energy per second is
d(dE)/dt = d(F dx ) dx = (dF/dt) dx + F d(dx/dt).
Is the above equation correct?
Is the calculation correct according to the picture above?
There is no calculation of energy loss per second for a fixed , degrading aging spring on the internet.
Thank you for your response.
Greetings ir. S.J. Boersen
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Python script for an aging spring calculation.
Download Python script AgingSpringPy.zip