Laplace transforms: Under-damped Mass-Spring System on an Incline

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Under-Damped Mass-Spring System on an Incline

Part 1 - Use Laplace Transformations

Problem Statement

Find the equation of motion for the mass in the system subjected to the forces shown in the Free Body Diagram (FBD).

Initial Conditions and Values

Equations of Equilibrium

Laplace Transform

Inverse Laplace Transform

Equation of Motion

Part 2 - Final and Initial Value Theorems

Initial Value Theorem

Final Value Theorem

Part 3 - Bode Plot

Part 4 - Breakpoints and Asymptotes on Bode Plot

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