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Assume that the system described by the differential equation mu+γ u+ku = 0 is critically damped and that the initial conditions are u(0) = u0, u(0) = v0. If v0 = 0, show that u…

Assume that the system described by the differential equation mu+γ u+ku = 0 is critically damped and that the initial conditions are u(0) = u0, u(0) = v0. If v0 = 0, show that u…
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Assume that the system described by the differential equation mu+γ u+ku = 0 is critically damped and that the initial conditions are u(0) = u0, u(0) = v0. If v0 = 0, show that u → 0 as t → [infinity] but that u is never zero. If u0 is positive, determine a condition on v0 that will ensure that the mass passes through its equilibrium position after it is released.

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User Ritesh D Joshi
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Answer:

V(o) < -[γu(o)]/2m

Step-by-step explanation:

I've attached the explanation.

Assume that the system described by the differential equation mu+γ u+ku = 0 is critically-example-1
Assume that the system described by the differential equation mu+γ u+ku = 0 is critically-example-2
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User Linehrr
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