Find the Transfer Function from the Dynamics

Calculus Level 4

Given the following dynamics relating $\theta$ and $y$ ,

$\dddot{\theta} +5\dot{\theta}-2\dot{y}+10\theta= \ddot{y}$

What is the transfer function from $y$ to $\theta$ , $\dfrac{\Theta (s)}{Y (s)}$ equal to?

\frac{s^{2}+2s}{s^{3}+5s+10 }

\frac{s^{2}+2s}{s^{3}+5s+s+10 }

\frac{s^{2}}{s^{3}+5s+2s+10 }

\frac{1}{s^{3}+5s+2s+10 }

1 solution

Samuel Hansen
Apr 10, 2017

The solution is found by taking the Laplace transform of both sides of the equation and we assume no initial conditions. Doing this and bringing the $\theta$ factors to the left and y factors to the right yields,

$\Theta s^{3}+ \Theta 5s + \Theta 10 = Y s^{2} +Y 2s$

Factoring $\theta$ and Y and dividing yields the desired result. Note that $\theta$ is the output and y is the input as it must be for this system to be causal.

Isn't the Laplace transform of a constant equal to the constant divided by "s", resulting in $\frac{10}{s}$ ?

Steven Chase - 4 years, 1 month ago

Yes! There is supposed to be a $\theta$ multiplying that 10! Sorry about that.

Samuel Hansen - 4 years, 1 month ago

Ok, just wanted to make sure I wasn't going crazy.

Steven Chase - 4 years, 1 month ago

I've corrected the problem.

Samuel Hansen - 4 years, 1 month ago

What is weird is that I chose the option that is in accordance with this solution and the answer is incorrect.

I chose the option: (s^2 +2s)/(s^3 + 5s + 10)

Is there some trick that I am missing here?

Karan Chatrath - 2 years, 8 months ago

i had the same problem

Youcef Mahdadi - 2 years, 5 months ago

Find the Transfer Function from the Dynamics

1 solution

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