# Simple harmonic motion

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This question is a long free-response question. Show your work for each part of the question. (15 points, suggested time 25 minutes)
A block slides back and forth on a track with a slight circular curvature, where friction is negligible, as shown above. The maximum height of the track at each end is much smaller than .
The center of mass of the block oscillates between and . The curve is so gradual that the total distance traveled along the curved portion of the track by the center of mass of the block can be considered to be
. At time the block is released from rest at position . The period of the block’s oscillation is 2.0 seconds.
Test Booklet
(a) Which of the graphs above, Graph 1 or Graph 2, could represent the block’s kinetic energy as a function of its position on the circular track, and which graph could represent the horizontal component of the net force acting on the block as a function of its position on the track? Justify both of your choices with physics principles.
(b) Choose one of the graphs in part (a) above and explain how the graph shows evidence that a restoring force is acting on the block.
AP Physics 1 Page 7 of 12

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Test Booklet
(c) Graph 3 above incorrectly shows the horizontal velocity of the block as a function of time. Identify a feature of the graph that does not correctly represent the motion of the block. Justify your answer.
(d) Track 2, shown above, has a horizontal length that is greater than that of Track 1 and the same maximum height . The block is released from rest at position Is the period of the block’s oscillation on Track 2 greater than, less than, or equal to the period of oscillation on Track 1? Justify your answer.
(e) A student derives the following equation for the period T of the block’s oscillation: , where is
the maximum displacement of the block from equilibrium and is the height of the track at . Whether or not this equation is correct, is the equation consistent with your answer to part (d)?