a) In the following, pick out the linear systems only. d²y dy d²y dy + y³ = u(t) i. + azy = 10 ii. + 5 dt2 dt dt2 + a1 dt d²y iii. y dt2 dy dy +a2у 3D 10 dt iv. dt + a¡y = azu(t)

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a) In the following, pick out the linear systems only.
d?y
i.
dt2
d²y
dy
+ a1
+ a2y = 10
ii.
+ 5
+ y³ = u(t)
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.
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 d²y dy + a1 + a2y = 10 ii. + 5 + y³ = u(t) 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. 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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