When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping, the new period T is such that
a. T < T0.
b. T = T0.
c. T > T0.
d. T < 0T0.
e. T > 0T0.
[Ques. 2] When a damping force is applied to a simple harmonic oscillator which has angular frequency 0 in the absence of damping, the new angular frequency is such that
a. < 0.
b. = 0.
c. > 0.
d. T < 0T0.
e. T > 0T0.
[Ques. 3] Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analog along the diameter of the acceleration of the particle executing simple harmonic motion is
a. the displacement from the center of the diameter of the projection of the position of the particle on the circle.
b. the projection along the diameter of the velocity of the particle on the circle.
c. the projection along the diameter of tangential acceleration of the particle on the circle.
d. the projection along the diameter of centripetal acceleration of the particle on the circle.
e. meaningful only when the particle moving in the circle also has a non-zero tangential acceleration.
[Ques. 4] 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.
[Ques. 5] 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.
[Ques. 6] A 2.00-m-long 6.00-kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0-kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency. The angular frequency (in s1) of the system of ladder and woman is
a. 1.01.
b. 3.07.
c. 4.03.
d. 8.05.
e. 16.2.
[Ques. 7] 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 1011 N/m2/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.
[Ques. 8] In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00-kg body vibrates at 1.00 Hz, a 2.00-kg body will vibrate at
a. 0.500 Hz.
b. 0.707 Hz.
c. 1.00 Hz.
d. 1.41 Hz.
e. 2.00 Hz.
[Ques. 9] The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be
a. 4 times as large.
b. 3 times as large.
c. 2 times as large.
d. the same as it was.
e. half as much.
[Ques. 10] The motion of a particle connected to a spring is described by x = 10 sin (t). At what time (in s) is the potential energy equal to the kinetic energy?
a. 0
b. 0.25
c. 0.50
d. 0.79
e. 1.0
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