phase constant, respectively. The argument of the cosine function, Ȧt + ij, is called the
phase. In sections that follow we will explain how these parameters are used to
describe SHM.
Graphing simple harmonic
motion
Cosine (or sine) function describes
displacementForthis graph:
x(t) = 3 cos (ʌt) meters
Simple harmonic motion
equation
x(t) = A cos (Ȧt + ij)
14.3 - Period and frequency
Period: Time to complete one full cycle of motion.
Frequency: Number of cycles of motion per second.
The period specifies how long it takes an object to complete one full cycle of motion. The letter T represents period, which is measured in
seconds. A convenient way to calculate the period is to measure the time interval between two adjacent peaks, as we do in Equation 1. In the
example shown there, it takes two seconds for the puck to complete one full cycle of motion.
The frequency, represented by f, specifies how many cycles are completed each second. It is the reciprocal of the period. The graph in
Equation 2 is the same as in Equation 1. Its frequency is 0.5 cycles per second.
Frequency has its own units. One cycle per second equals one hertz (Hz). This unit is named after the German physicist Heinrich Hertz
(1857í1894). You may be familiar with the hertz units from computer terminology: The speed of computer microprocessors used to be
specified in megahertz (one million internal clock cycles per second) but microprocessors now operate at over one gigahertz (one billion cycles