
X = 2 · cos ( 4 π • t)


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The equation you've provided is in the form of X = 2 * cos(4π * t), which represents a periodic function where X is the dependent variable, t is the independent variable (usually time), and π represents the mathematical constant pi.
In this equation, X represents the amplitude of a cosine wave, and it's twice the amplitude of a typical cosine wave (which has an amplitude of 1). The frequency of the cosine wave is determined by the coefficient in front of t, which is 4π. This means the wave completes four full cycles (oscillations) within a unit interval of t. The standard period for a cosine function is 2π, but here, it's compressed to 2π / (4π) = 1/4 of its usual length.
If you were to graph this equation, you'd see a cosine wave that oscillates much faster than a typical cosine wave, completing four full cycles within the usual 2π interval. The amplitude is doubled, so the wave reaches a maximum value of 2 and a minimum value of -2. The frequency of oscillation is 4 times greater than the standard cosine wave.


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