period = 2, Amplitude = 2
AMPLITUDE
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f(t) = sin(t) , this function has an amplitude of 1 , because its y values goes one unit up, and one unit down from the x axis. to increase this to an amplitude of 2, we get f(t) = 2. sin(t). This means the graph is twice as tall as our original function f(t) = 1.sin(t).
PERIOD
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the period has a formula: w = 2pi / |B | . The normal period for a sinewave
f(t) = sin(t) = 2 pi.
So in our new function f(t) = 2 sin (t) [ amplitude is now multiplied by 2], the period (as stated in the question) is 2, that is 2 pi (remember the formula for period stated 2pi) divided by b, which is now 2. Which means 2pi is now divided by 2 or multiplied by 1/2. 2pi /2 = pi or 1/2 x 2pi = pi. so as you increase the period in the equation, the sinewave becomes shorter.
ANSWER
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So the function is actually f(t) = 2.sin(2t).