Find the undamped position too pls A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position xo and initial velocity vo. Find theposition function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t)=C₁e Pl cos (@t-₁). Also, find the undamped position function u(t) = Cocos (@ot-o) that would result if the mass on the spring were set in motion with the same initial position andvelocity, but with the dashpot disconnected (so c= 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t).3m==17₁ c = 2₁ k = 2₁ x₁ = 3₁ v₁ = 0Dx(t)=, which means the system is(Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 andless than or equal to 2x.)

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x(t) = . which means the system is (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.)

x(t) = . which means the system is (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.)

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.52P: A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where...

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