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If disturbed its behavior depends on the damping ratio ζ. If the damping ratio is zero there is no dissipation of energy and the system will oscillate at its natural frequency indefinitely—harmonic motion. If the damping ratio is not zero, the disturbed system will tend back to equilibrium, in an oscillatory fashion if the damping ratio is less than unity (underdamped) and without oscillations if the damping ratio is greater than unity (overdamped). The “frequency” of the oscillations in the underdamped case is less than the natural frequency.

Dry friction is essential for stopping your car. Disc brakes work by forcing a pair of calipers to grip a disk rigidly attached to the wheel. The disk moves with respect to the calipers as long as the car is still moving, so the force on the disk depends on the coefficient of sliding friction. This friction force exerts a torque on the wheel, which causes it to slow down. The car slows because of the friction between the tire and the ground. Ultimately (as some tire commercials have pointed out) brakes don’t stop your car: tires do.

17). One can see the beat frequency, and about two and one half of these appear in the figure. 025 ¼ 80π, so there will be two and one half long periods in 200π, as shown in the figure. The period of the entire function according to Eq. 05π. Exercises 17 Fig. 8 Response of the function in Eq. 975 Exercises 1. Write the kinetic and potential energies of a body falling freely under gravity. Denote the position of the mass by z. Let the mass of the body be a mass scale. Choose a length scale L. Let the energy scale be mgL.

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