8 Given differential equation of a dynamic system below. Please obtain analytical expression for the system frequency response in the polar form and show the phase: * d'y(1) dt Sd²y(t) dr? 4dy(t) 2d²x(1) 7dx(1) + 16y (t) dt + 20x (t) dt tan-Aw-jw? 16-5w4 7w2 O phi (w) = tan 20-2w phi (w) = tan-'( ) - tan- ) 4w 8-5w2 4w-jw phi (w) = tan-'( ) - tan-( ) 7w 20-2w2 16-5w2 4w-jw ( ) - tan-" () 7w O phi (w) = tan 10-2w) - tan 8-5w?

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8
Given differential equation of a dynamic system below. Please obtain analytical expression for
the system frequency response in the polar form and show the phase: *
d'y(1)
dt
Sd²y(t)
dr?
4dy(t)
2d²x(1)
7dx(1)
+ 16y (t)
dt
+ 20x (t)
dt
tan-Aw-jw?
16-5w4
7w2
O phi (w) = tan
20-2w
phi (w) = tan-'( ) - tan- )
4w
8-5w2
4w-jw
phi (w) = tan-'( ) - tan-( )
7w
20-2w2
16-5w2
4w-jw
( ) - tan-" ()
7w
O phi (w)
= tan
10-2w) - tan
8-5w?
Transcribed Image Text:8 Given differential equation of a dynamic system below. Please obtain analytical expression for the system frequency response in the polar form and show the phase: * d'y(1) dt Sd²y(t) dr? 4dy(t) 2d²x(1) 7dx(1) + 16y (t) dt + 20x (t) dt tan-Aw-jw? 16-5w4 7w2 O phi (w) = tan 20-2w phi (w) = tan-'( ) - tan- ) 4w 8-5w2 4w-jw phi (w) = tan-'( ) - tan-( ) 7w 20-2w2 16-5w2 4w-jw ( ) - tan-" () 7w O phi (w) = tan 10-2w) - tan 8-5w?
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