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Examples:

Examples:. R 2. R 1. L. C. -. +. V 1 (t). V 2 (t). Write the transfer function of the electrical circuit including Op-Amp ( Op erational Amp lifier). Write the Matlab program to calculate the eigenvalues of the system. clc;clear a=[120 412 7500]; roots(a). Examples:. f(t).

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Examples:

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  1. Examples: R2 R1 L C - + V1(t) V2(t) Write the transfer function of the electrical circuit including Op-Amp (Operational Amplifier). Write the Matlab program to calculate the eigenvalues of the system. clc;clear a=[120 412 7500]; roots(a)

  2. Examples: f(t) a) Find the transfer function. b) Find the response to the input in the form of f(t)=40e-4t . x(t) k c c) Find the response to the input in the form of f(t)=40cos(3t-1). d) Find the response to the input in the form of f(t)=100e-2tcos(5t+1). k=4000 N/m, c=50 Ns/m e) Find the response to the input in the form of f(t)=10δ(t) (Impulse input with magnitude 10 Ns) f) Find the response to the input in the form of f(t)=50u(t) (Step input with magnitude 50 N) g) Write the form of the exponential input, for which the system works at resonance. b) a) The equation of motion of the system whose mass can be neglected is given as

  3. Examples: Img Img Re Re >>s=3i; >>hs=1/(50*s+4000) >>gen=abs(hs) >>fi=angle(hs) c) f(t)=40cos(3t-1)  s=3i φH >>s=-2+5i; >>hs=1/(50*s+4000) >>gen=abs(hs) >>fi=angle(hs) d) f(t)=100e-2tcos(5t+1)  s=-2+5i φH

  4. Examples: e) f(t)=10δ(t) Residue Theorem clc;clear num=[1]; den=[1 80 0]; [r,p,k]=residue(num,den) f) f(t)=50u(t)

  5. Examples: Steady State Value xss=0.0125 The resonance condition does not depend on the input amplitude A. g) Exponential input for resonance; The s value, which makes the denominator of the transfer function zero causes the system resonance. The s value for resonance is s=-80. So, the form of the exponential function for resonance condition is

  6. Examples: Consider the electrical circuit including Op-Amp. Where v1 is the input and v2 is the output a) Find the Laplace transform of the output V2(s) to a step input with magnitude 12 V. Calculate the steady-state value of the output v2ss . b) Write the matlab code to calculate the |H(s)| and φHs for an exponential-harmonic input in the form of v1(t)=24e-0.2t cos(5t-0.2). clc;clear s=-0.2+5i; hs=-2500/(120*s^2+412*s+7500); hg=abs(hs) hfi=angle(hs)

  7. Examples: Img xss=-2 Re -2 or Steady-state value -3 In the calculation procedure of a system response, the result of the Matlab command [r,p,k]=residue(pay,payda) gives the r and p vectors as r=-2+3i, -2-3i, 6, -2 ve p=-4+6i,-4-6i, -3, 0. Find the system response x(t) using the given r and p. Find the steady-state response.

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