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function u (t) == C, cos(@ot – ao) 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 = Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 0). 15. m = ;, c = 3, k = 4; xo = 2, vo = 0 %3D

function u (t) == C, cos(@ot – ao) 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 = Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 0). 15. m = ;, c = 3, k = 4; xo = 2, vo = 0 %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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function u (t) = Co cos(wot - ao) 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 = Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 0). 15. m = ;, c = 3, k = 4; xo = 2, vo = 0 16. m = 3, c = 30, k = 63; xo = 2, vo = 2 17. m = 1, c = 8, k = 16; xo = 5, vo = -10 18. m = 2, c = 12, k = 50; xo = 0, vo = -8 m%3= %3D %3D 160: x 16
Transcribed Image Text:function u (t) = Co cos(wot - ao) 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 = Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 0). 15. m = ;, c = 3, k = 4; xo = 2, vo = 0 16. m = 3, c = 30, k = 63; xo = 2, vo = 2 17. m = 1, c = 8, k = 16; xo = 5, vo = -10 18. m = 2, c = 12, k = 50; xo = 0, vo = -8 m%3= %3D %3D 160: x 16
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dash- pot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo Find the position function x(t) and determine whether the mo- tion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) = C1e¬P! cos(@t- a1). Also, find the undamped position %3D
Transcribed Image Text:The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dash- pot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo Find the position function x(t) and determine whether the mo- tion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) = C1e¬P! cos(@t- a1). Also, find the undamped position %3D
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