(Solved): .21. A machine part is modeled as a pendulum connected to a spring as illustrated in Figure P1.21. ...

.21. A machine part is modeled as a pendulum connected to a spring as illustrated in Figure P1.21. Ignore the mass of the pendulum's rod and derive the equation of motion. Then following the procedure used in Example 1.1.1, linearize the equation of motion and compute the formula for the natural frequency. Assume that the rotation is small enough so that the spring only deflects horizontally. Figure P1.21