Figure 10.b 11. Consider a system described the following equation y(t)= [cos t+sin t]x(t) i. Is this system linear? ii. Is this system time invariant? iii. Determine the response to the input 8(t–) 12. a) Draw f-i analogous electrical network of the mechanical system in Figure 12.a and write the equations of motions in terms of given mechanical quantities. Assume that

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t=0
t=1
1H
92
v. (t)
1Ω
Figure 10.b
11. Consider a system described the following equation y(t)= [cos t+sin t]x(t)
i. Is this system linear?
ii. Is this system time invariant?
iii. Determine the response to the input d(t – 5)
12. a) Draw f-i analogous electrical network of the mechanical system in Figure 12.a and
write the equations of motions in terms of given mechanical quantities. Assume that
the bar is massless and the junctions are restricted to have vertical motion.
f=Fcos(0+t)
M4
M3
U1
D1
D2
U2
U3
K3
M1
K2
D2
D3
K,
K,
M2
Figure 12.a
12. b) Draw the T-i analogous electrical circuit of the rotational mechanical system shown in Figure 12.b and find the
expression for the corresponding angular rotation.
Page 5 of 7
00
Transcribed Image Text:t=0 t=1 1H 92 v. (t) 1Ω Figure 10.b 11. Consider a system described the following equation y(t)= [cos t+sin t]x(t) i. Is this system linear? ii. Is this system time invariant? iii. Determine the response to the input d(t – 5) 12. a) Draw f-i analogous electrical network of the mechanical system in Figure 12.a and write the equations of motions in terms of given mechanical quantities. Assume that the bar is massless and the junctions are restricted to have vertical motion. f=Fcos(0+t) M4 M3 U1 D1 D2 U2 U3 K3 M1 K2 D2 D3 K, K, M2 Figure 12.a 12. b) Draw the T-i analogous electrical circuit of the rotational mechanical system shown in Figure 12.b and find the expression for the corresponding angular rotation. Page 5 of 7 00
Ω
Ko2
lo1
Ω
De2
De1
Figure 12.b
13. a) Find the Fourier series expansion of the periodic wave shown in Figure 13.a. Sketch
frequency and phase spectrum also.
A x(t)
1-
O o o o
O o o o
2n
Figure 13.a
+00
13. b) Show that energy of an aperiodic signal can be expressed as E = ||X(@)do,where X(@) represents the
-00
Fourier transform of x(t).
13. c) Show that 1 > 2r8(a@)
14. a) Consider the communication system in Figure 14.a. Find the spectrum of y(t).
sin@ht
cosoht
Xo(t)
H(@)
y(t)
x(t)
H(@)
Xs(t)
sinot
coso,t
H(@)
* X(@)
0.5-
1
-Ob
Figure 14.a
Page 6 of 7
+,
Transcribed Image Text:Ω Ko2 lo1 Ω De2 De1 Figure 12.b 13. a) Find the Fourier series expansion of the periodic wave shown in Figure 13.a. Sketch frequency and phase spectrum also. A x(t) 1- O o o o O o o o 2n Figure 13.a +00 13. b) Show that energy of an aperiodic signal can be expressed as E = ||X(@)do,where X(@) represents the -00 Fourier transform of x(t). 13. c) Show that 1 > 2r8(a@) 14. a) Consider the communication system in Figure 14.a. Find the spectrum of y(t). sin@ht cosoht Xo(t) H(@) y(t) x(t) H(@) Xs(t) sinot coso,t H(@) * X(@) 0.5- 1 -Ob Figure 14.a Page 6 of 7 +,
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