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 initialvelocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position functionin the form x(t) = C₁ e¯pt cos (@₁t-x₁). Also, find the undamped position function u(t)= Cocos (@ot-) that would result if the mass on the spring were set in motion withthe same initial position and velocity, 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).m= 1, c = 8, k = 16, xo = 6, Vo = - 18Cx(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 thanor equal to 0 and less than or equal to 2л.)

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