John says that the value of the function cos(t + T) + , obtained one period T after time t, is greater than cos(t + ) by 2. Larry says that it is greater by the addition of 1.00 to cos(t + ). Which one, if either, is correct?
a. John, because T = 2.
b. John, because T = 1 radian.
c. Larry, because T = 2.
d. Larry, because T = 1 radian.
e. Neither, because cos( + 2) = cos.
Question 2
Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?
a. Ellen, because 2 is directly proportional to the constant multiplying the displacement and to the mass.
b. Ellen, because 2 is directly proportional to the mass.
c. Mary, because 2 is directly proportional to the constant multiplying the displacement and to the mass.
d. Mary, because 2 is directly proportional to the mass.
e. Mary, because the second derivative of an oscillatory function like sin(t) or cos(t) is always proportional to the negative of the original function.
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Use the graph of the function f(x) to answer each question.