Forced Vibration of Cart attached to Wall by Spring/Problem Definition
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Definition of Problem
Consider a cart $C$ of mass $m$ attached to a wall by means of a spring $S$.
Let $C$ be free to move along a straight line in a medium which applies a damping force $\mathbf F_d$ whose magnitude is proportional to the speed of $C$.
Let the force constant of $S$ be $k$.
Let the constant of proportion of the damping force $\mathbf F_d$ be $c$.
Let there be applied to $C$ an external force which varies as a function of time as:
- $\mathbf F_e = \mathbf F_0 \cos \omega t$
where $\mathbf F_0$ is constant.
Let the displacement of $C$ at time $t$ from the equilibrium position be $\mathbf x$.
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.20$: Vibrations in Mechanical Systems$