How Do You Transform f(t) = cos(t) for t>=2 Using Step Functions?

AI Thread Summary
The discussion focuses on transforming the function f(t) = cos(t) for t ≥ 2 into terms of step functions. The initial equation is defined as f(t) = 0 for t < 2 and f(t) = cos(t) for t ≥ 2. A solution presented is f(t) = cos(t)u(t-2), where u(t-2) is the unit step function that activates at t = 2. The challenge lies in correctly applying the shift for the step function. The consensus confirms that the transformation is accurate, with the unit step function becoming 1 at t = 2.
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Homework Statement


just trying to get the below equation in terms of step functions, just not sure how to get the cos(t) with the same shifted variable
f(t) = 0 for t<2 f(t)=cos(t) t>=2


The Attempt at a Solution


this is what i got
cos(t)u(t-2)
just having troubles working out the shift for it, had no problems doing this sort of question when it was a multiple of pi, but this has stumped me!
thanks in advance
 
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You got it correct, cos(t)u(t-2).
When t = 2, then u(t-2) = u(0), which is where the unit step becomes 1.
 
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