(A)
(B)
(C)
(D)
(E)
Answers
1 . D —Neither the pendulum nor the mass-spring system’s time period is dependent on the amplitude of
the release point, so
.
2 . D —The equation of motion of the oscillating mass is x = A (cosωt ), where the amplitude (A ) = 6
m. The cos function repeats itself when Time (t ) = 4 s. This occurs when 2π = ωt = ω(4 s). Therefore,
ω = π/2. Taking the second derivative of the position function yields the acceleration of the mass:
. Thus, the magnitude of the maximum acceleration is .
3 . D —The potential energy of the system is given by . Note that the potential energy is
always positive. This eliminates all the graphs except choices D and E. The potential energy will be
at a maximum when the velocity of the mass is zero. This corresponds to choice D. Choice E
represents the kinetic energy of the system.4 . C —Since the mass of the pendulum is distributed throughout its length, we must use the physical
pendulum formula . The moment of inertia for a uniform bar is and = .