Question

The mass $m$ in Figure P4.62 is attached to a rigid rod having an inertia $I$ about the pivot and negligible pivot friction. The input is the displacement $z$. When $z = \theta = 0$, the spring is at its free length. Assuming that $\theta$ is small, I: moment of inertia of the rod a) State all the assumptions and presumptions draw the free body diagram (label magnitude and direction of any vector) with presumptions included; derive the Equation of Motion for the System and its respective Transfer Function. b) Using MATLAB and the Laplace method to obtain the solution to the ODE for the displacement input (step function $z(t) = 0.25 \ u(t)$) with $m = 3kg$, $c = 5N-s/m$, $k = 100N/m$, $L1 = L2 = 0.6m$, $L3 = 1.5m$ $I = 1.8$ Plot the solution. (Analytical solution and Matlab code) c) Using $tf()$ and $step()$ functions along with the Transfer Function found in a) and the parameters given in b) to plot the response of the system to the specified input. Compare results. (print code)

          The mass $m$ in Figure P4.62 is attached to a rigid rod having an inertia $I$ about the pivot and negligible pivot friction. The input is the displacement $z$. When $z = \theta = 0$, the spring is at its free length. Assuming that $\theta$ is small,

I: moment of inertia of the rod
a) State all the assumptions and presumptions draw the free body diagram (label magnitude and direction of any vector) with presumptions included; derive the Equation of Motion for the System and its respective Transfer Function.
b) Using MATLAB and the Laplace method to obtain the solution to the ODE for the displacement input (step function $z(t) = 0.25 \ u(t)$) with $m = 3kg$, $c = 5N-s/m$, $k = 100N/m$, $L1 = L2 = 0.6m$, $L3 = 1.5m$ $I = 1.8$ Plot the solution. (Analytical solution and Matlab code)
c) Using $tf()$ and $step()$ functions along with the Transfer Function found in a) and the parameters given in b) to plot the response of the system to the specified input. Compare results. (print code)

The mass m in Figure P4.62 is attached to a rigid rod having an inertia I about the pivot and negligible pivot friction. The input is the displacement z. When z = θ = 0, the spring is at its free length. Assuming that θ is small,

I: moment of inertia of the rod
a) State all the assumptions and presumptions draw the free body diagram (label magnitude and direction of any vector) with presumptions included; derive the Equation of Motion for the System and its respective Transfer Function.
b) Using MATLAB and the Laplace method to obtain the solution to the ODE for the displacement input (step function z(t) = 0.25 u(t)) with m = 3kg, c = 5N-s/m, k = 100N/m, L1 = L2 = 0.6m, L3 = 1.5m I = 1.8 Plot the solution. (Analytical solution and Matlab code)
c) Using tf() and step() functions along with the Transfer Function found in a) and the parameters given in b) to plot the response of the system to the specified input. Compare results. (print code)

Added by Alexandria S.

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