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sin (Nut v(1) = E sin [(wn + now)t sin sin (4) 1. Let dw = 0.01 and wn = 1, and plot V(t) for N = 5, N = 10 and N = 25 on separate axes. 2. Give a brief comment on the relationship of N and the shape of the plots. 3. For Small values of dw, W(t) can be written as 2 sin hut )sin with f(t): Sut Plot V(t) of Equation (1) and f(t) on the same set of axes. Take dw = 0.01, N = 10 and wn = 1. %3D %3D

sin (Nut v(1) = E sin [(wn + now)t sin sin (4) 1. Let dw = 0.01 and wn = 1, and plot V(t) for N = 5, N = 10 and N = 25 on separate axes. 2. Give a brief comment on the relationship of N and the shape of the plots. 3. For Small values of dw, W(t) can be written as 2 sin hut )sin with f(t): Sut Plot V(t) of Equation (1) and f(t) on the same set of axes. Take dw = 0.01, N = 10 and wn = 1. %3D %3D

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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sin Nut sin (쪽) V(t) = sin [(an + nou)t) = sin !3! 1. Let dw = 0.01 and wn = 1, and plot V(t) for N = 5, N = 10 and N = 25 on separate axes. 2. Give a brief comment on the relationship of N and the shape of the plots. 3. For Small values of dw, V(t) can be written as 2 sin (N+1) w(t) = f(t) sin with f(t) Sut Plot V(t) of Equation (1) and f(t) on the same set of axes. Take dw = 0.01, N = 10 and w= 1. 4. Is t =0 a root of f(t)? Why (not)? 5. Find the expression for the roots of f(t). Hint: sin 6 = 0 implies 6 = ma uhere m = 0, +1, +2, --. 6. Define At := 2t, where t, is the first positive root of f(t). (a) Write At in terms of duw and N. (b) Define Aw := (N + 1)ów and find the value of AwAt. 7. Prove equation (1). Hint: Use one of the trigomametric identities for sin and use sin (Ne sin () sin Ne N N Esin(n6): Ne sin (쓸) and com(ne) = N6 COR sin ()
Transcribed Image Text:sin Nut sin (쪽) V(t) = sin [(an + nou)t) = sin !3! 1. Let dw = 0.01 and wn = 1, and plot V(t) for N = 5, N = 10 and N = 25 on separate axes. 2. Give a brief comment on the relationship of N and the shape of the plots. 3. For Small values of dw, V(t) can be written as 2 sin (N+1) w(t) = f(t) sin with f(t) Sut Plot V(t) of Equation (1) and f(t) on the same set of axes. Take dw = 0.01, N = 10 and w= 1. 4. Is t =0 a root of f(t)? Why (not)? 5. Find the expression for the roots of f(t). Hint: sin 6 = 0 implies 6 = ma uhere m = 0, +1, +2, --. 6. Define At := 2t, where t, is the first positive root of f(t). (a) Write At in terms of duw and N. (b) Define Aw := (N + 1)ów and find the value of AwAt. 7. Prove equation (1). Hint: Use one of the trigomametric identities for sin and use sin (Ne sin () sin Ne N N Esin(n6): Ne sin (쓸) and com(ne) = N6 COR sin ()
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