Question

Problem 3: Consider the following pendulum that consists of massless straight rigid rod AOB with a point mass m attached at the bottom point A. The pendulum rotates without friction about the point O and it is initially at vertical equilibrium. A spring k is attached at the top point B and sets the pendulum to motion with the application of a vertical displacement input z(t). The spring k is unstretched at t = 0 and the pendulum is vertical a) Determine the linearized equation of motion of the pendulum b) Compute the transfer function from the displacement input z(t) to the angular displacement $\theta$(t) of the pendulum $G(s) = \frac{\Theta(s)}{Z(s)}$ c) Suppose that z(t) is a unit step input. Find the rotational motion $\theta$(t) of the pendulum as a function of the system parameters. What is the maximum horizontal displacement $x_{max}$ of the mass m from the horizontal equilibrium?

          Problem 3: Consider the following pendulum that consists of massless straight rigid rod AOB with a
point mass m attached at the bottom point A. The pendulum rotates without friction about the
point O and it is initially at vertical equilibrium. A spring k is attached at the top point B and sets the
pendulum to motion with the application of a vertical displacement input z(t). The spring k is
unstretched at t = 0 and the pendulum is vertical
a) Determine the linearized equation of motion of the pendulum
b) Compute the transfer function from the displacement input z(t) to the angular displacement
$\theta$(t) of the pendulum $G(s) = \frac{\Theta(s)}{Z(s)}$
c) Suppose that z(t) is a unit step input. Find the rotational motion $\theta$(t) of the pendulum as a
function of the system parameters. What is the maximum horizontal displacement $x_{max}$ of
the mass m from the horizontal equilibrium?

Problem 3: Consider the following pendulum that consists of massless straight rigid rod AOB with a
point mass m attached at the bottom point A. The pendulum rotates without friction about the
point O and it is initially at vertical equilibrium. A spring k is attached at the top point B and sets the
pendulum to motion with the application of a vertical displacement input z(t). The spring k is
unstretched at t = 0 and the pendulum is vertical
a) Determine the linearized equation of motion of the pendulum
b) Compute the transfer function from the displacement input z(t) to the angular displacement
θ(t) of the pendulum G(s) = (Θ(s))/(Z(s))
c) Suppose that z(t) is a unit step input. Find the rotational motion θ(t) of the pendulum as a
function of the system parameters. What is the maximum horizontal displacement xmax of
the mass m from the horizontal equilibrium?

Added by Encarnacion B.

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