The spring pendulum is characterized by the spring constant D, the mass m
and the constant of attenuation G.
(G is a measure of the friction force assumed
as proportional to the velocity.) It is a question of finding the size of the resonator's elongation y (compared with its mid-position) at the time t. Using w_{0} = (D/m)^{1/2} this problem is described by the following differential equation:
If you want to solve this differential equation, you have to distinguish between several cases:
y(t) = A_{abs} sin (wt)
+ A_{el} cos (wt)
+ e^{-Gt/2}
[A_{1} sin (w_{1}t)
+ B_{1} cos (w_{1}t)] y(t) = (A_{E} w t / 2) sin (wt) y(t) = A_{abs} sin (wt)
+ A_{el} cos (wt)
+ e^{-Gt/2}
(A_{1} t + B_{1}) y(t) = A_{abs} sin (wt)
+ A_{el} cos (wt)
+ e^{-Gt/2}
[A_{1} sinh (w_{1}t)
+ B_{1} cosh (w_{1}t)] URL: http://home.a-city.de/walter.fendt/phys/resmathengl.htm |
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