Obtain the transfer function for the following differential equation and check whether the input free solution is stable or not, d x d t + 3 x = f ( t )

Name: Obtain the transfer function for the following differential equation and check whether the input free solution is stable or not, d x d t + 3 x = f ( t )
Uploaded: 2022-02-23T17:22:57+00:00
Description: Obtain the transfer function for the following differential equation and check whether the input free solution is stable or not, d x d t + 3 x = f ( t )

Question

Obtain the transfer function for the following differential equation and check whether the input free solution is stable or not,            d      x              d      t        +  3  x  =  f  (  t  )

Davin Meyer · Accepted Answer

Just solve it in Laplace:            x      ˙        +  3  x  =  f  (  t  )Applying Laplace transform and derivative property   {            f      ˙        (  t  )  }  =  s  F  (  s  )  −  f  (  0  ), considering initial condition f(0)=0 :  s  X  (  s  )  +  3  X  (  s  )  =  F  (  s  )  X  (  s  )  (  s  +  3  )  =  F  (  s  )  Y  (  s  )  =            X      (      s      )              F      (      s      )        =      1          s      +      3      Using the transform   {      1          s      +      a        }  =      e          −      a      t        y  (  t  )  =      e          −      3      t      Finally, you can see that it&#039;s stable. In fact the only pole of the function (  s  =  −  3) is negative. This is clear on the time axis too, because the transient response goes to zero as t goes to infinity.

Obtain the transfer function for the following differential equation (dx)/(dt)+3x=f(t)

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