Question

A particular system's dynamics is governed by below equation, where x(t) is the output and f(t) is the input. Determine the system's transfer function. *+*+jx(7)dt = f(t)

Answer 1

FINDING A SYSTEM'S TRANSFER FUNCTION,

T
+
T
+
[ r(t)dt
= f (t)

T
+
T
+
T Sie (t)dt
= f (t)

T
+
T
+
2
$\times$ t² = f (t)

1. Choose what is the input and what is the output,

here, x (t) = output and f(t) = input

2. Take Laplace transform assuming zero ICs,

L (
T
) = s² x(t) + S
T
₍₀₎ +
T
₍₀₎

S
T
₍₀₎ ,  
T
₍₀₎ are zero because there are cancel.

This process are so on and get,

S² x_(t)+ Sx_(t) = f(t)

3. Rearrange than we get,

output input
=   
2 f(t)
= S² + S