Thread: Transfer function by differential equation

How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?


d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

Originally Posted by moisesbr

How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?


d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

For mathematical type setting we use LaTeX, the tutorial is here

CB

Originally Posted by moisesbr

How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?


d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

Write this as:



Then if we assume that at time that the input and out put and all relevant derivatives are zero, and we take the Laplace transform of the above equation we get:



then the transfer function is:



CB

How did you pass from first to second line below ?

Sorry for the silly question but I've been a long time out of maths
and I having a hard time to remind all in a new course I am starting

Thanks for your patience

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

Originally Posted by moisesbr

How did you pass from first to second line below ?

Sorry for the silly question but I've been a long time out of maths
and I having a hard time to remind all in a new course I am starting

Thanks for your patience

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

It is just another notation for the derivatives:



CB