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 w0 = (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) = Aabs sin (wt)
+ Ael cos (wt)
+ e-Gt/2
[A1 sin (w1t)
+ B1 cos (w1t)]
y(t) = (AE w t / 2) sin (wt)
y(t) = Aabs sin (wt)
+ Ael cos (wt)
+ e-Gt/2
(A1 t + B1)
y(t) = Aabs sin (wt)
+ Ael cos (wt)
+ e-Gt/2
[A1 sinh (w1t)
+ B1 cosh (w1t)] URL: http://home.a-city.de/walter.fendt/phys/resmathengl.htm |
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