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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

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1
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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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2
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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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3
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4-1-q5

The graph represents the acceleration a as a function of time t for a simple harmonic oscillator.

In which of the positions shown on the graph is the displacement of the oscillator zero?

  • Position A

  • Position B

  • Position C

  • Position D

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4
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An oscillation is set up to begin from equilibrium.

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

A is a cosine displacement time graph. B is a negative sine displacement time graph. C is a sine velocity time graph. D is a negative cosine acceleration time graph.

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    5
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    Which of the following graphs represents the speed V as a function of displacement x for a particle performing simple harmonic motion?

    q8_4-1_mcq_medium_ib-physics-sl

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      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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      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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      3
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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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      4
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      An oscillation is set up to begin at a positive maximum displacement x subscript 0.

      Which of the following graphs could represent the velocity v of the oscillation as a function of time t?

      All options have velocity on the y axis and time on the x axis. Option A is a cosine graph (initial positive non zero velocity then decreasing). option B is a negative sine graph (initial velocity of zero then negative values). Option C is a sine graph (initial velocity of 0, then positive values). Option D is a negative cosine graph (initial negative non zero velocity then increasing).

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        5
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        A cosine graph of displacement against time. Point A is when the graph passes through the x axis a second time. Point B is the second peak of the graph (the first being at t=0). Point C is the third time the graph passes through the x axis. Point D is the second minimum of the graph.

        A simple pendulum is set into oscillatory motion when a student pulls the bob to the left and releases it from a small angle. The graph represents the displacement of the bob as a function of time.

        At which position on the graph is the velocity of the bob directed towards the right?

        • Position A

        • Position B

        • Position C

        • Position D

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        1
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        A cosine shape on a displacement time graph. A is at the first time the graph crosses the x axis. B is at the first minimum. C is between the second crossing of the x axis but before the second maximum. D is at the same height as C, but on the other side of the maximum.

        The graph represents the displacement as a function of time for a particle performing simple harmonic oscillations.

        At which position on the graph does the particle's acceleration and velocity act in opposite directions?

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          2
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          Sine graph of θ against time. First ,minimum occurs at 5s and third maximum occurs at 15s. Maximum θ is roughly 2.8 degrees, minimum is -2.8 degrees.

          The graph represents the angle made by a pendulum from the vertical as a function of time.

          Which of the following is most nearly the length of the pendulum?

          • 1 space straight m

          • 7 space straight m

          • 10 space straight m

          • 11 space straight m

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          3
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          A horizontal mass-spring system oscillates in simple harmonic motion. The mass is released at t space equals space 0, and 1.25 space seconds later, the magnitude of the acceleration is zero and its displacement is 3.0 space cm.

          Which of the following expressions represents the displacement xof the mass as a function of time t?

          • x space equals space 0.06 space sin space open parentheses 2.5 straight pi t close parentheses

          • x space equals space 0.06 space cos space open parentheses 0.40 straight pi t close parentheses

          • x space equals space 0.03 space cos space open parentheses 0.40 straight pi t close parentheses

          • x space equals space 0.03 space sin space open parentheses 2.5 straight pi t close parentheses

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          4
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          A spring-mass system oscillates with frequency 0.50 space Hz. The spring has a spring constant of 160 space straight N divided by kg and the object attached to the spring has a mass of 0.40 space kg. At equilibrium, the speed of the object is 2.0 space straight m divided by straight s.

          Which of the following is most nearly the time taken for the object to be displaced from 0 space cm to 3.5 space cm?

          • 0.01 space straight s

          • 0.1 space straight s

          • 0.4 space straight s

          • 0.5 space straight s

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          5
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          A cosine displacement time graph with a period of 1s and a maximum of 4 cm at t=0s. The amplitude of oscillations decreases over time, so each maxima is shorter than the last. The maximum is 1 cm at t=5s.

          The graph shows the displacement as a function of time for a mass-spring system undergoing simple harmonic motion where friction is introduced into the system at time t space equals space 0 space straight s. The spring constant of the spring is 140 space straight N divided by kg.

          Which of the following is most nearly the average rate of energy loss of the system from t space equals space 0 to t space equals space 5 space straight s?

          • 20 space mW

          • 30 space mW

          • 40 space mW

          • 50 space mW

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