The following data is provided for the translational mechanical system considered in Problem 2.11.

Use MATLAB to find the following:

(a) The output response (y) to an input force of $50N$.

(b) The response to an impulse force input.

(c) If the values of $b_1$ and $b_2$ were variables, choose values of $b_1$ and $b_2$ that will reduce oscillations, give practical settling time, and produce smooth responses.

If the output was the platform displacement $x_3$, obtain the new matrices $C$ and $D$.

(a) Find the output response (y) to an input force of $50N$.

(b) Find the response to an impulse force input.

(c) If the values of $b_1$ and $b_2$ were variables, choose values of $b_1$ and $b_2$ that will reduce oscillations, and give practical settling time and smooth responses.

Data from Problem 2.11

Consider the following mechanical system.

The forces exerted by the springs are zero when \(x_{1}=x_{2}=x_{3}=0\). The input force is \(f(t)\) and the absolute displacements of \(m_{1}, m_{2}\), and \(m_{3}\) are \(x_{1}, x_{2}\), and \(x_{3}\), respectively.

Transcribed Image Text:

m = 5kg m2 = 15kg m3 = 50kg b = 500N/m/s b = 600N/m/s k = 5,000N/m k = 10,000N/m