TEST PROBLEMS MECHANICAL ENGINEERING

TEST PROBLEMS MECHANICAL ENGINEERING

Question #1

A uniform bar of length L and weight W is suspended symmetrically by two unstrechable strings as shown in the figure.  If the bar is given small initial rotation about the vertical axis,

a.       Draw the free body diagram of the bar during its free oscillation.

b.      Write down the equation of motion for small angular oscillation about axis O-O.

c.       Determine the period of the free oscillation of the bar.

Question #2

The system shown in the figure is in its static equilibrium position (SEP). It consists of a uniform rod of mass M and length L and is supported by spring of stiffness K and dashpot of coefficient C.

1. Draw the free body diagram of each system as it oscillates about the SEP.
2. Derive the equation of motion of each system using Newton’s second law.
3. Determine the undamped natural frequency.
4. Determine the damping ratio, the critical damping coefficient, and the damped natural frequency.

Question #3

The system shown consists of a cylinder of mass M with a piston, which imparts resistance proportional to the velocity of a linear viscous damping C, the cylinder is restrained by a spring of stiffness K 

(a) draw the free body diagram of the cylinder,

(b) write down the equation of motion using Newton’s second law, and

(c) determine the response amplitude and phase angle using Complex Algebra.