SIMPLE HARMONIC MOTION There are certain oscillations that can be described as simple harmonic motion or SHM. This is the name given to oscillatory motion for a system whenever the net force can be described by Hooke’s law. This is referred to as a simple harmonic oscillator. As long as there is no damping of the motion by friction or other forces, this type of oscillator will oscillate with equal displacement on either side of the equilibrium position. The maximal displacement is referred to as the amplitude, identified by the letter X. The units of amplitude are the same as they are for displacement, which are meters for objects like a spring but, for sound oscillations, the units will be in pressure units. The amplitude is related to the energy stored in the oscillation. An object that is attached to a spring which is sliding along a frictionless surface is a simple harmonic oscillator. The amplitude will be X and the period will be T. The maximum speed occurs as it passes through its equilibrium point. The stiffer the spring, the smaller the period will be. The greater the mass of the object, the greater is the period. The period and the frequency are, as mentioned, related to one another but neither are related to the amplitude of the spring. A guitar string will make the same sound regardless of how hard it is struck. Because the period will be constant, a simple harmonic oscillator can be used to run a clock. The period will be related to the stiffness of the system because of its force constant. High stiffnesses have high force constants and a smaller period. In addition, more massive systems will increase the period (think of a heavier person bouncing more slowly on a diving board). Mass and the force constant are the only factors that affect the period and the frequency of things in simple harmonic motion. This is defined according to figure 95:
209
