AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 7: OscillationsRepresenting and Analyzing SHM

Representing and Analyzing SHM (College Board AP® Physics 1: Algebra-Based)

Exam Questions

5 mins5 questions
1
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An object-spring oscillator is initially at rest. A student displaces the object from equilibrium and releases it. The object then oscillates with simple harmonic motion, reaching a maximum velocity of v subscript m a x end subscript.

If the initial displacement is defined as the negative direction, which of the following expressions correctly represents the change in the object's velocity at time t?

  • negative v subscript m a x end subscript sin open parentheses 2 straight pi f t close parentheses

  • v subscript m a x end subscript sin open parentheses 2 straight pi f t close parentheses

  • negative v subscript m a x end subscript cos open parentheses 2 straight pi f t close parentheses

  • v subscript m a x end subscript cos open parentheses 2 straight pi f t close parentheses

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2
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Graph showing velocity (y-axis) vs. time (x-axis) with a sinusoidal wave. Velocity is initially 0, then decreases to a minimum and returns to 0 at a time of T/2. Velocity then increases to a maximum then returns to zero at a time T. Velocity decreases and then increases back to 0 at a time of 3T/2. Velocity increases and then decreases back to zero at time 2T.

The graph shows the velocity of a pendulum as a function of time.

Which of the following correctly represents the time at which the acceleration of the pendulum is at a maximum value?

  • 0

  • T over 2

  • fraction numerator 3 T over denominator 4 end fraction

  • fraction numerator 5 T over denominator 4 end fraction

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3
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A block attached to a horizontal spring oscillates on a surface with negligible friction at a frequency of 0.75 Hz. The spring is initially displaced from equilibrium, and after 3.2 s, the displacement of the block is 12 cm.

Which of the following is most nearly the amplitude of the oscillation?

  • 0.12 m

  • 0.15 m

  • 0.20 m

  • 0.40 m

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4
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A block is suspended from a spring and shown at different times. The positive direction is upwards. At t = 0, the block is at a middle height. At t = T/4, the block is higher. At t = T/2, the block is back at middle height. At t = 3T/4, the block is lower. At t = T, the block is at middle height again.

A block on a vertical spring performs simple harmonic oscillations.

Which of the following graphs could represent the acceleration a of the block as a function of time t?

  • A graph of acceleration against time shows a sinusoidal graph. This starts at a = 0, increases to a maximum and then returns to a = 0 at t = T/2. The graph then reaches a minimum and returns to a = 0 for t = T.
  • A graph of acceleration against time shows a sinusoidal graph. This starts at maximum acceleration, decreases to a = 0 and then decreases to minimum acceleration at t = T/2. The graph then increases to a = 0 and then further until acceleration is maximum at t = T.
  • A graph of acceleration against time shows a sinusoidal graph. This starts at a = 0, decreases to a minimum and then returns to a = 0 at t = T/2. The graph then reaches a maximum and returns to a = 0 for t = T.
  • A graph of acceleration against time shows a sinusoidal graph. This starts at minimum acceleration, increases to a = 0 and then increases further to maximum acceleration at t = T/2. The graph then decreases to a = 0 and then decreases further until acceleration is minimum at t = T.

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5
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Which of the following statements is true for a child playing on a frictionless swing that periodically reaches a maximum angular displacement of 30°?

  • The restoring torque is provided by tension.

  • Angular acceleration is directly proportional to the angular displacement.

  • The angular displacement is directly proportional to the restoring torque.

  • The relationship between angular acceleration and angular displacement is not directly proportional.

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