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 w2 is directly proportional to the constant multiplying the displacement and to the mass.
b. Ellen, because w2 is directly proportional to the mass.
c. Mary, because w2 is directly proportional to the constant multiplying the displacement and to the mass.
d. Mary, because w2 is directly proportional to the mass.
e. Mary, because the second derivative of an oscillatory function like sin(wt) or cos(wt) is always proportional to the negative of the original function.
Question 2
Suppose it were possible to drill a frictionless cylindrical channel along a diameter of the Earth from one side of the Earth to another. A body dropped into such a channel will only feel the gravitational pull of mass within a sphere of radius equal to the distance of the mass from the center of the Earth. The density of the Earth is 5.52 103 kg/m3 and G = 6.67 10-11 Nm2/kg2 . The mass will oscillate with a period of
a. 84.4 min.
b. 169 min.
c. 24.0 h.
d. 1 130 h.
e. 27.2 d.
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