Free Damped Oscillations A mass m is attached to both a spring (with given spring constant) and a dashpot (with given damping constant c). The equation that governs this system is given by mx" + cx + kx = 0. The mass is set in motion with initial conditions x and vo. For each of the equations below: • Determine whether the motion is overdamped, critically damped, or underdamped. • Find the position function x(t) and If it is underdamped, write the position function in the form x(t) = C₁e¯pt cos (wit - α1). • Find the undamped position function u(t) = Cocos (wot - α0) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t).

Free Damped Oscillations A mass m is attached to both a spring (with given spring constant) and a dashpot (with given damping constant c). The equation that governs this system is given by mx" + cx + kx = 0. The mass is set in motion with initial conditions x and vo. For each of the equations below: • Determine whether the motion is overdamped, critically damped, or underdamped. • Find the position function x(t) and If it is underdamped, write the position function in the form x(t) = C₁e¯pt cos (wit - α1). • Find the undamped position function u(t) = Cocos (wot - α0) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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