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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 7: OscillationsEnergy of Simple Harmonic Oscillators

Energy of Simple Harmonic Oscillators (College Board AP® Physics 1: Algebra-Based)

Exam Questions

5 mins5 questions
1
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An ion in a crystal lattice structure oscillates with simple harmonic motion. The period of the oscillation is T which is measured from equilibrium.

Which of the following graphs shows the change in kinetic energy of the ion from time t = 0 to t = T over 2?

Four graphs labeled A, B, C, and D display different waveforms with time (t) on the x-axis and energy (E) on the y-axis. Graph A: E increases from 0 to a maximum, returns to zero, drops to a negative minimum and then returns to 0 at a time of T/2. Graph B: E starts at a maximum, drops to zero and returns to a maximum at time T/2 Graph C: E starts at a maximum, drops to zero, returns to the maximum a second time, drops to zero and finishes at a third maximum at time T/2 Graph D: E starts at zero, increases to a maximum and then decreases to zero again by time T/2

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2
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A mass is attached to a vertical spring and allowed to reach equilibrium. It is then displaced by a distance d and released. The total energy and time period are E subscript t o t end subscript and T respectively. In a second investigation, the same mass-spring system oscillates but travels twice as fast through equilibrium.

Which line correctly identifies the total energy and time period of the new oscillations, E subscript t o t comma n e w end subscript and T respectively?

E subscript t o t comma n e w end subscript

T subscript n e w end subscript

A

2 E subscript t o t end subscript

T over 2

B

4 E subscript t o t end subscript

T over 2

C

2 E subscript t o t end subscript

2 T

D

4 E subscript t o t end subscript

T

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3
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Two systems each feature a horizontal spring attached to a wall. In both systems, a block of mass m is attached to the free end of the spring. The first system has a spring constant k. The second system has a spring constant 4k. Both blocks are at equilibrium (x = 0) travelling rightwards with the same speed v_max.

Two object-spring systems oscillate on horizontal, frictionless surfaces, as shown in the figure. The first system oscillates with amplitude A.

Which of the following expressions correctly represents the amplitude of the second system?

  • A over 2

  • A

  • 2 A

  • 4 A

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4
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A block-spring system oscillates horizontally with an amplitude of 8 m.

When the displacement of the block from equilibrium is 5 m, which of the following is most nearly the ratio of the kinetic energy to potential energy of the system?

  • 0.4

  • 0.6

  • 1.6

  • 2.6

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5
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An energy bar chart is shown with three bars. The first bar, labelled U_s is three quarters the height of the axis. The second bar, labelled K, is one quarter of the height of the y axis. The third bar, labelled U_G, has a height of zero.

An object-spring-Earth system oscillates vertically in simple harmonic motion. The energy bar chart in the figure shows the elastic potential energy U subscript s, kinetic energy K, and gravitational potential energy U subscript G of the object at the equilibrium position.

Which of the following most closely represents the energy bar chart of the system when the object is at the lowest point of the oscillation?

Graph A: U_s is nearly the full height of the positive axis, K has zero height and U_G is small and positive. Graph B: U_s is zero, K is the full height of the positive axis and U_G is half the height of the positive axis. Graph C: U_s is taller than the positive axis, K is zero and U_G is negative and a quarter of the height of the negative axis Graph D: U_s is three quarters the height of the positive axis, K is zero and U_G is negative and three quarters the height of the negative axis

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