5. (a) a mass of 20 grams stretches a spring 5cm. suppose that the mass is also attached to a damper with constant coeficient 0.4 n-s/m. initially the mass is pulled down an additional 2cm and released. write the initial- value problem for the position u(t) of the mass at time t. do not solve this equation. the solution to a differential equation that models a vibrating spring is u(t) 4e-: cos(a) +3c" sin(3t) + ? ? cos(2) + " sin(2) (b) determine the transient part of the solution; phase, quasi-amplitude, quasi-frequency and quasi-period of the transient part. (c) determine the steady state part of the solution; phase, amplitude, frequency and period of the steady part 6. find the general solution of the differentin ouunti