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a) In the following, pick out the linear systems only. d²y i. dt2 d?y dy + a1 + y³ = u(t) + a2y = 10 ii. + 5 dt dt2 dt d²y iii. y dt2 dy dy + azy = 10 dt iv. + a1y dt azu(t) b) In the following, pick out the nonlinear systems only. (4 marks) 2 dy + d2. 1 dy t dt i. + y = 10 dt ii. + a1y azu(t) dt2, d³y d²y + + dt2 d²y iv. dt2 dy + y? = 10 dy ii. + y = 20 dt dt3 dt d²x c) b) A model of a system is dx +2 dt2 + 6х 3D 5. Find x(t) as t -> со. X(0) — 1, х (0) — 0. dt

a) In the following, pick out the linear systems only. d²y i. dt2 d?y dy + a1 + y³ = u(t) + a2y = 10 ii. + 5 dt dt2 dt d²y iii. y dt2 dy dy + azy = 10 dt iv. + a1y dt azu(t) b) In the following, pick out the nonlinear systems only. (4 marks) 2 dy + d2. 1 dy t dt i. + y = 10 dt ii. + a1y azu(t) dt2, d³y d²y + + dt2 d²y iv. dt2 dy + y? = 10 dy ii. + y = 20 dt dt3 dt d²x c) b) A model of a system is dx +2 dt2 + 6х 3D 5. Find x(t) as t -> со. X(0) — 1, х (0) — 0. dt

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.5: Cramer's Rule
Problem 35PS
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a) In the following, pick out the linear systems only. d?y i. dt2 d?y dy + a1 + a2y = 10 ii. + 5 + y³ = u(t) dt dt2 dt d²y iii. y dt2 dy dy + azy = 10 dt iv. + a1y azu(t) dt b) In the following, pick out the nonlinear systems only. (4 marks) d2. 1 dy t dt dy i. + + y = 10 ii. + a1y azu(t) dt d33 d²y + + dt2 d2, iv. dt2 dy + y? = 10 dy ii. + y = 20 dt dt3 dt d²x + 2 dt2 dx c) b) A model of a system is + 6х 3D 5. Find x(t) as t -> со. X(0) — 1, х (0) — 0. dt 6+j7 d) Obtain the real and imaginary parts of Z = 3-j4 Also, obtain the magnitude and angle of this complex quantity.
Transcribed Image Text:a) In the following, pick out the linear systems only. d?y i. dt2 d?y dy + a1 + a2y = 10 ii. + 5 + y³ = u(t) dt dt2 dt d²y iii. y dt2 dy dy + azy = 10 dt iv. + a1y azu(t) dt b) In the following, pick out the nonlinear systems only. (4 marks) d2. 1 dy t dt dy i. + + y = 10 ii. + a1y azu(t) dt d33 d²y + + dt2 d2, iv. dt2 dy + y? = 10 dy ii. + y = 20 dt dt3 dt d²x + 2 dt2 dx c) b) A model of a system is + 6х 3D 5. Find x(t) as t -> со. X(0) — 1, х (0) — 0. dt 6+j7 d) Obtain the real and imaginary parts of Z = 3-j4 Also, obtain the magnitude and angle of this complex quantity.
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