A function g(t) has the following description. It is zero for t < ? 5. It has a slope of –2 in the range ? 5 < t < ?2. It has the shape of a sine wave of unit amplitude and with a frequency of 1/4 Hz plus a constant in the range ? 2 < t < 2. For t > 2 it decays exponentially toward zero with a time constant of 2 seconds. It is continuous everywhere.

Question

(a) Write an exact mathematical description of this function.
(b) Graph g(t) in the range ? 10 < t < 10.
(c) Graph g(2t) in the range ? 10 < t < 10.
(d) Graph 2g (3 ? t) in the range ? 10 < t < 10.
(e) Graph ? 2g ( (t + 1) / 2) in the range ? 10 < t < 10.

Answer 1

Solutions: