This problem is in 5 parts. Part 1: Derive the leading differential equation for

Question

This problem is in 5 parts.
Part 1: Derive the leading differential equation for the system from the motion equations. The equation shall be expressed with ? and its time derivatives

Part 2: Express the rod (S) in ? and its time derivatives.

Part 3: Write an expression for total mechanical energy , E , for whole system.

Is rotaional energy needed in the expression? If it is, then why? Explain your equation of the rotational energy.

The leading differential equation can now being formulated through the following:

Now , perform this operation with the expression you did got from 1: in the begining.

Part 5: Solve the problem in MatLab.

If you are able to solve this problem.
Please use the numbers for each solve. Like "1: "solution" 2: "solution" since there are 5 subquestions that helps leading to the 5th question.

Explanation / Answer

when a body rotates about a fixed axis , any point p in the body travels along a circula path, the angula position of p is defined by theta.

the change in angula position Dtheta, is called the angular displacement , with units of either radians or revolutions . they are related by

1 revolutio = 2pie radians

angular velocity , w = is obtained by taking the time derivative of angular displacement w = dtheta /dt (rad/s) + similarly anglar acceleration is

alpha = d2theta / dt2 = dw / dt or alpha = w(dw/dtheta) + mmentum rad/s2

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