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 x 0 and initial velocity v 0. Find the position 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)equalsUpper C 1 e Superscript negative pt Baseline cosine left parenthesis omega 1 t minus alpha 1 right parenthesis. ​Also, find the undamped position function ​u(t)equalsUpper C 0 cosine left parenthesis omega 0 t minus alpha 0 right parenthesis 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 cequals​0). ​Finally, construct a figure that illustrates the effect of damping by comparing the graphs of​ x(t) and​ u(t). mequals1​, cequals10​, kequals25​, x 0equals4​, v 0equalsnegative 5 Question content area bottom Part 1 ​x(t)equals    4 e Superscript negative 5 t Baseline plus 15 t e Superscript negative 5 t​, which means the system is critically damped. ​(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 2pi​.) Part 2 The undamped position is ​u(t)equals    4.1231 cosine left parenthesis 5 t minus 6.0382 right parenthesis. ​(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 2pi​.)