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Consider the following initial value problem: y" + 10y' + 50y = h(t); y(0) = 0, y(0) = 5; %3D S 50,

Consider the following initial value problem: y" + 10y' + 50y = h(t); y(0) = 0, y(0) = 5; %3D S 50,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following initial value problem: y" + 10y' + 50y = h(t); y(0) = 0, y/(0) = 5; 了 50、st<警 0st< ort2等 h(t) = 0, (a) Sketch the graph of the forcing function on an appropriate interval. 60 59 58 57 560 55 54 53 52 51 50 (b) Find the solution of the given initial value problem. NOTE: Denote the two Heaviside functions by u(t) and ua(t). Indicate separately the values of c and d knowing that c is the minimum of the two values. y(t) = where c = d = (c) Use a graphing utility to view the graph of the solution. (d) Explain how the graphs of the forcing function and the solution are related. The solution starts out as free oscillation, due to the initial conditions. The amplitude Choose one as long as the forcing is present. Thereafter, the solution (Choose one
Transcribed Image Text:Consider the following initial value problem: y" + 10y' + 50y = h(t); y(0) = 0, y/(0) = 5; 了 50、st<警 0st< ort2等 h(t) = 0, (a) Sketch the graph of the forcing function on an appropriate interval. 60 59 58 57 560 55 54 53 52 51 50 (b) Find the solution of the given initial value problem. NOTE: Denote the two Heaviside functions by u(t) and ua(t). Indicate separately the values of c and d knowing that c is the minimum of the two values. y(t) = where c = d = (c) Use a graphing utility to view the graph of the solution. (d) Explain how the graphs of the forcing function and the solution are related. The solution starts out as free oscillation, due to the initial conditions. The amplitude Choose one as long as the forcing is present. Thereafter, the solution (Choose one
ts out as froo oscillation due to the initia Choose d Choose one rcing is grows solution rapidly decays remains constant
Transcribed Image Text:ts out as froo oscillation due to the initia Choose d Choose one rcing is grows solution rapidly decays remains constant
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