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Nicci
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Show, from the first principles, that the equation of motion of a mass (m) on a spring, subjected to a linear resistance force R, a restoring force S, and a driving force G(t) is given by
d2x/dt2+ 2K(dx/dt) + Ω2x = F(t)
I started by saying S = αx and R = βv.
ma = G(t) - S - R = G(t) - αx - βv where a = (d2x/dt2) and v = (dx/dt)
I am a bit confused on how to use the first principles to derive the equation. Usually for first principles I would have a function like f(x) and then I would use f(x+h), but I am stuck on this part. I did try to use G(t) and G(t+h), but that did not work.
Can someone maybe give me a hint on how to use the first principles in this case? I am sure I will be able to derive the equation if I can just figure out the next step.
Thank you very much in advance.
Show, from the first principles, that the equation of motion of a mass (m) on a spring, subjected to a linear resistance force R, a restoring force S, and a driving force G(t) is given by
d2x/dt2+ 2K(dx/dt) + Ω2x = F(t)
I started by saying S = αx and R = βv.
ma = G(t) - S - R = G(t) - αx - βv where a = (d2x/dt2) and v = (dx/dt)
I am a bit confused on how to use the first principles to derive the equation. Usually for first principles I would have a function like f(x) and then I would use f(x+h), but I am stuck on this part. I did try to use G(t) and G(t+h), but that did not work.
Can someone maybe give me a hint on how to use the first principles in this case? I am sure I will be able to derive the equation if I can just figure out the next step.
Thank you very much in advance.
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