Question

14. Consider the initial value problem where y is the damping coeficient (or resistance). (a) Let γ =-. Find the solution of the initial value problem and plot its graph. (b) Find the time t, at which the solution attains its maxi mum value. Also find the maximum value y, of the solution. (c) Let γ = 4 and repeat parts (a) and (b). (d) Determine how ti andy, vary as γ decreases. What are the values of, and y, when γ = 0? Problem 14 in $5.7 of Brannan and Boyce (p.350 in 3rd ed. text). Also complete part (e) if take γ-- and replace the forcing term, δ(t-1), with a sum ΣΝι δ(t-kd), what d should we pick to maximize the amplitude of the response? Solve the problem with this d and plot your solution for .

Answer 1

14. Consider the initial value problem where γ is the damping coefficient (or resistance) (a) Let γ =-. Find the solution of the initial value problem and plot its graph 6(y')-«V (a)-y (0) Ca sY (s) sy(0)-(0) Y () s (0) (0)+(Y() (0)2 - e5 S 2st1) 七 (b) Find the time t at which the solution attains its maxi- mum value. Also find the maximum value y, of the solution. ⓘanď repeat parts(a)and (b) Cv-Y()(0) C{y")-say (s) sy(0) y'(0) SY () s (0) (0)+(Y (s) (0)Y4-e 4 e e. (4s4) (d) Determine how 11 and vi vary as γ decreases.