Hello everyone 
I have an exercise to do in electronics about transfer function and frequency transfer function...
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For system described by differential equation:
1) [MATH] [/MATH][MATH]10y'(t) + y(t) = u(t)[B][B] [/B][/B][/MATH]
2) [MATH][/MATH][MATH]5y'(t) + y(t) = 2u'(t)[B][/B][/MATH]
Determine:
a) Transfer function G(s)
b) Frequency transfer function G(jw) and Nyquist diagram
c) Impulse response g(t)
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My answer:
For the first equation: [MATH]10y'(t) + y(t) = u(t)[/MATH]
a) [MATH]G(s) = \frac{output}{input} = \frac{Y(s)}{U(s)} = \frac{10s + 1}{1} = 10s + 1[/MATH]b) We substitute [MATH] s = jw [/MATH] : [MATH] G(jw) = 10jw + 1[/MATH]c) [MATH] g(t) = L^{-1} {G(s)} [/MATH] = [MATH] L^{-1} (10s + 1) [/MATH]I'm blocking here - I don't know how to solve it...
For the second equation: [MATH]5y'(t) + y(t) = 2u'(t)[/MATH]a) [MATH] G(s) = \frac{output}{input} = \frac{Y(s)}{U(s)} = \frac{5s + 1}{2s} = \frac{5}{2} + \frac{1}{s}[/MATH]b) We substitute [MATH] s = jw [/MATH] : [MATH] G(jw) = \frac{5}{2} + \frac{1}{jw} [/MATH]c) [MATH] g(t) = L^{-1} {G(s)} [/MATH] = [MATH] L^{-1} \frac{5}{2} + \frac{1}{s} [/MATH]I'm blocking here - I don't know how to solve it...
My main problem is the maths... about the Laplace. Can you help me please ?
Thank you,
CloudNine,
I have an exercise to do in electronics about transfer function and frequency transfer function...
"
For system described by differential equation:
1) [MATH] [/MATH][MATH]10y'(t) + y(t) = u(t)[B][B] [/B][/B][/MATH]
2) [MATH][/MATH][MATH]5y'(t) + y(t) = 2u'(t)[B][/B][/MATH]
Determine:
a) Transfer function G(s)
b) Frequency transfer function G(jw) and Nyquist diagram
c) Impulse response g(t)
"
My answer:
For the first equation: [MATH]10y'(t) + y(t) = u(t)[/MATH]
a) [MATH]G(s) = \frac{output}{input} = \frac{Y(s)}{U(s)} = \frac{10s + 1}{1} = 10s + 1[/MATH]b) We substitute [MATH] s = jw [/MATH] : [MATH] G(jw) = 10jw + 1[/MATH]c) [MATH] g(t) = L^{-1} {G(s)} [/MATH] = [MATH] L^{-1} (10s + 1) [/MATH]I'm blocking here - I don't know how to solve it...
For the second equation: [MATH]5y'(t) + y(t) = 2u'(t)[/MATH]a) [MATH] G(s) = \frac{output}{input} = \frac{Y(s)}{U(s)} = \frac{5s + 1}{2s} = \frac{5}{2} + \frac{1}{s}[/MATH]b) We substitute [MATH] s = jw [/MATH] : [MATH] G(jw) = \frac{5}{2} + \frac{1}{jw} [/MATH]c) [MATH] g(t) = L^{-1} {G(s)} [/MATH] = [MATH] L^{-1} \frac{5}{2} + \frac{1}{s} [/MATH]I'm blocking here - I don't know how to solve it...
My main problem is the maths... about the Laplace. Can you help me please ?
Thank you,
CloudNine,