Q:

5.1 Determine the transformation for the constants of integration C ₁, C ₂ so that Eq. (5.3a) can be written in terms of a cosine function rather than a sine function.

Q:

5.2 (a) Redo Example 5.1 using the Lagrange equations and the following two generalized coordinates: u( t) measured upward at the center of mass and ?( t) measured counterclockwise about the center of mass. Obtain the matrix equations of motion.

(b) Redo part (a), but this time use Newton s equations of motion to write the matrix equations of motion.

(c) Redo part (a), but this time use as DOF u ₁( t) ? v( t), the upward deflection of the left-hand end of the system, and ?( t) the counterclockwise rotation about the left-hand end of the system.

(d) Redo part (c), but this time use Newton s equations of motion to write the matrix equations of motion.

Q:

5.3 Write the equation for the equivalent viscous damping coefficient for the following types of damping forces.

(a) Coulomb damping. (Also see Exercises 5.8 and 5.9.)

(b) A damping force for which the energy dissipated per cycle is independent of frequency and proportional to the amplitude of the vibration raised to the 1.75 power. (This represents a fluid drag force acting on a cylinder for a Reynolds number range from 4 to 1000.)

Q:

5.4