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Amp period shift - Transformations Given any functional...

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Transformations Given any functional relationship y =f(t), the effect on that relationship by replacing f(t) with f(c t), f(t+c), c f(t), f(t)+c, or a combination of these is away of interest. The first three are of particular interest for the circular functions and have particular names associated with them. Changing the period and frequency. The contrast between sin t and sin c t is that, depending on the specific value of c , the period will change from 2 π to a different value. For example, sin 3t is the y -coordinate of P(3t). Since P will wrap around the unit circle one when 3t=2 π , t= is the period of sin 3 t . This can be seen from the graph of the first periods of sin t (dashed) and sin 3t (solid). A smaller period implies a higher frequency , which measures the number of times the wrapping function point rotates around the unit circle per unit time. While sin t has frequency , sin 3t has a higher frequency, . In general, frequency = .
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