In circuit theory, a filter is an electrical network that alters the amplitude a

Question

In circuit theory, a filter is an electrical network that alters the amplitude and/or phase characteristics of an input signal with respect to frequency. The following circuit in Fig.1 is an example of band-reject or notch filter. This assignment studies the function of this filter.

the differential equation of the system can be written as

the differential equation of the system can be written as

Let the input voltage be cos(t) and assume initial conditions to be zero. Solve the system equation to find the output response using MATLAB command 'dsolve'.

I want Matlab code for solving the above differential equation using MATLAB command 'dsolve'

Please help in generating the code. I have tried, but getting error.

Explanation / Answer

>> clear all

>> syms x y t

>> x=cos(t)

x =

cos(t)

>> dsolve('D2y+Dy+100*y=D2x+100*x')

ans =

cos(10*t)*int(-sin(10*t)*(10*y(t) + diff(y(t), t)/10 + diff(y(t), t, t)/10), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + C3*cos(10*t) + C4*sin(10*t) + sin(10*t)*((cos(10*t)*diff(y(t), t))/10 + y(t)*(cos(10*t)/10 + sin(10*t)) + int(sin(10*t)*y(t), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))

>> simplify(ans)

ans =

y(t) + sin(10*t)*int(sin(10*t)*y(t), t) + C3*cos(10*t) + C4*sin(10*t) + cos(10*t)*int(cos(10*t)*y(t), t)

>> int(cos(10*t)*y, t)

ans =

(y*sin(10*t))/10

>> int(sin(10*t)*y, t)

ans =

-(y*cos(10*t))/10

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