(Solved): .35. A foot pedal mechanism for a machine is crudely modeled as a pendulum connected to a spring a ...

.35. A foot pedal mechanism for a machine is crudely modeled as a pendulum connected to a spring as illustrated in Figure P1.35. The purpose of the spring is provide a return force for the pedal action. Compute the spring stiffness needed to keep the pendulum at $$1^{?}$$ from the horizontal and then compute the corresponding natural frequency. Assume that the angular deflections are small, such that the spring deflection can be approximated by the arc length; that the pedal may be treated as a point mass; and that pendulum rod has negligible mass. The pedal is horizontal when the spring is at its free length. The values in the figure are $$m=0.5\mathrm{kg},g=9.8\mathrm{m}/{\mathrm{s}}^2,l_1=0.2\mathrm{m}$$, and $$l_2=0.3\mathrm{m}$$. Figure P1.35