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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 7: OscillationsSimple Harmonic Motion

Simple Harmonic Motion (College Board AP® Physics 1: Algebra-Based): Exam Questions

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1
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A pendulum displaced from amplitude A oscillates at frequency f.

If the pendulum is stopped and displaced from a new amplitude of fraction numerator 3 A over denominator 2 end fraction, which of the following correctly describes the period of this new motion?

  • fraction numerator 3 f over denominator 2 end fraction

  • fraction numerator 2 over denominator 3 f end fraction

  • space f

  • 1 over f

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2
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A simple pendulum and a mass-spring system oscillate about their equilibrium positions with simple harmonic motion. On Earth, the period of both oscillations is T. The pendulum and the mass-spring system are taken to Mars, which is a less massive planet.

Which of the following rows best describes the period of the pendulum and the mass-spring system on Mars?


Simple Pendulum

Mass-spring System

A

T

greater than T

B

T

T

C

greater than T

greater than T

D

greater than T

T

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    3
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    Which of the following statements is not true about the displacement of an object oscillating in simple harmonic motion?

    • Displacement is a vector quantity.

    • Displacement and velocity act in opposite directions.

    • Displacement is proportional to the restoring force.

    • Displacement is proportional to acceleration.

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    4
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    Which of the following is not a condition of simple harmonic motion?

    • The restoring force is in the same direction as displacement.

    • Acceleration is directed toward the equilibrium position.

    • The oscillations are isochronous.

    • The magnitude of the restoring force is proportional to the displacement.

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    5
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    A pendulum is undergoing simple harmonic motion with a time period T and angular frequency omega. A student makes a change to the setup so that the pendulum has a new time period 3 T.

    Which of the following expressions represents the new angular frequency?

    • 6 omega

    • 3 omega

    • omega over 3

    • omega over 6

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    1
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    An block of mass m is suspended from a vertical spring of spring constant k. When the system is in equilibrium, the spring has a length of 20 cm. The block is displaced 12 cm from its equilibrium position before it is released.

    If the initial displacement is defined as the positive direction, which of the following expressions correctly describes the acceleration of the block at the instant it is released?

    • negative fraction numerator 0.32 m over denominator k end fraction

    • negative fraction numerator 0.12 k over denominator m end fraction

    • fraction numerator 0.12 k over denominator m end fraction

    • fraction numerator 0.32 k over denominator m end fraction

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    2
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    q4_4-1_mcq_medium_ib-physics-sl

    A particle P oscillates in simple harmonic motion along the line XZ about equilibrium point Y, as shown in the figure.

    Which of the following statements is true about the particle's motion at point P?

    • It has maximum kinetic energy and minimum potential energy.

    • The total energy is equal to the kinetic energy at X.

    • The particle is accelerating as the restoring force acts towards Y.

    • The particle is accelerating as the restoring force acts towards X.

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    3
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    A block connected to a horizontal spring which is connected to a wall. The spring has length 10 cm.

    A mass is attached to a spring which has an original unstretched length of 10 cm. The other end of the spring is attached to a wall. The string is stretched and released, setting it into oscillatory motion along the horizontal surface. In the figure shown above, the mass is moving to the left.

    In which of the following directions does the spring force act when the mass is in the position shown?

    • To the left

    • To the right

    • Upwards

    • No direction because the spring force is zero.

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    4
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    A simple pendulum consisting of a bob of mass 500 space straight g attached to a string of length 2.5 space straight m is fixed to the ceiling. The pendulum is displaced by a small angle and released.

    Which of the following is most nearly the time taken for the pendulum to reach its vertical equilibrium position for the first time?

    • 0.4 space straight s

    • 0.8 space straight s

    • 1.6 space straight s

    • 3.2 space straight s

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    5
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    A pendulum shown at two stages of its motion. At t_0, it is at its amplitude position on the left. At t_1 it is at the central equilibrium position.

    A pendulum consisting of a rope and a mass is released from rest at time t subscript 0, as shown in the figure. The mass is at the lowest height in the swing at time t subscript 1.

    Assuming the pendulum begins with negative displacement but is traveling in the positive direction, which of the following correctly describes how the angular acceleration of the pendulum changes at time t subscript 0 and time t subscript 1?

    Change in angular acceleration at t subscript 0

    Change in angular acceleration at t subscript 1

    A

    Decreasing

    Increasing

    B

    Decreasing

    Decreasing

    C

    Increasing

    Increasing

    D

    Increasing

    Decreasing

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      1
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      A metal object connected to the end of a spring of spring constant k oscillates with amplitude A on a horizontal, frictionless surface. A coin is placed on the metal object, such that the two have a combined mass of M subscript t o t end subscript. The coefficient of static friction between the coin and the metal object is mu subscript s.

      Which of the following shows the position of oscillation at which the coin could slip on the metal object and the value of the coefficient of static friction required for this to happen?

      Position of Oscillation

      Coefficient of Static Friction

      A

      Amplitude Position

      mu subscript s space less than space fraction numerator k A over denominator M subscript t o t end subscript g end fraction

      B

      Equilibrium Position

      mu subscript s space less than space fraction numerator k A over denominator M subscript t o t end subscript g end fraction

      C

      Amplitude Position

      mu subscript s space less than space fraction numerator M subscript t o t end subscript g over denominator k A end fraction

      D

      Equilibrium Position

      mu subscript s space less than space fraction numerator M subscript t o t end subscript g over denominator k A end fraction

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        21 mark

        A spring-object harmonic oscillator consists of an object of mass m and a spring of constant k. A pendulum, suspended from a horizontal rod, has a period equal to half of the spring-object oscillator's period and a maximum angular displacement of 6°.

        Which of the following expressions correctly represents the minimum vertical distance between the pendulum bob and the rod?

        • m g open parentheses fraction numerator 1 over denominator 4 k end fraction close parentheses cos open parentheses 6 degree close parentheses

        • m g open parentheses fraction numerator 1 over denominator 4 k end fraction close parentheses

        • 4 m g open parentheses 1 over k close parentheses sin open parentheses 6 degree close parentheses

        • 2 m g open parentheses 1 over k close parentheses cos open parentheses 6 degree close parentheses

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        3
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        A mass is attached to a spring from above and the spring is secured to a clamp. The mass is pulled down and released resulting in a simple harmonic oscillation. 

        Which one of the following statements is true about the motion of the mass?

        • The tension in the spring is at a minimum as the mass passes through the equilibrium position.

        • The total potential energy in the system is at a maximum when the mass is at the highest point of its oscillation.

        • The acceleration of the mass is at a maximum as it passes through the equilibrium position.

        • The kinetic energy is at a minimum when the mass is at the lowest point in its oscillation.

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        4
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        A simple pendulum is set into small oscillatory motion on Earth. It is then set into small oscillatory motion on a spacecraft that orbits at a distance from the Earth's center that is twice the Earth's radius. The length of the pendulum is also doubled.

        What is the ratio of the pendulum's frequency on the spacecraft to its frequency on Earth, f subscript s p a c e end subscript over f subscript e a r t h end subscript?

        • 2

        • 1 half

        • square root of 2

        • fraction numerator square root of 2 over denominator 4 end fraction

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        5
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        A pendulum shown in three different positions. In position X, the mass is at the leftmost side of its swing. In position Y the string is vertical. In position Z the mass is at the rightmost side of its swing.

        A simple pendulum consisting of a sphere attached to a string is suspended from the ceiling, as shown in the figure. The pendulum is initially displaced from position Z and swings to position X.

        Which of the following gives the direction of the net acceleration of the sphere at position Y?

        • To the left

        • Upwards

        • To the right

        • No direction because the acceleration is zero

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