Notes of ODE Recitations
نویسنده
چکیده
Here, • m > 0 is the mass. • k > 0 is the spring constant and the spring force −ku(t) is modeled to be proportional to u(t) (i.e. Hooke’s law). The minus sign shows that it is always a restoring force which pulls the mass back towards the equilibrium. • γ ≥ 0 is the damping constant. The damping force may come from the medium (e.g. air, water, or honey), the spring or other sources. It has a minus sign since it prevents the mass from moving. • F (t) is the external force, assumed to be independent of u. • Initial data could be provided as well, e.g. u(0) = u0 and u′(0) = v0.
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