IBPhysics: HLDPTopic Questions9. Wave Phenomena (HL only)9.1 Simple Harmonic Motion

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First teaching 2014

Last exams 2024

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Simple Harmonic Motion (DP IB Physics: HL)

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9.1 Simple Harmonic Motion

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9.1 Simple Harmonic Motion

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1
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Which equation is used for calculating the displacement as a function of time for an oscillator that begins its oscillation from the equilibrium position?

  • x space equals space x subscript 0 sin omega t

  • v space equals space omega x subscript 0 cos omega t

  • a space equals space minus omega squared x subscript 0 sin omega t

  • a space equals space minus omega x

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2
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Which graph correctly shows how the kinetic energy of an oscillator varies as a function of time through one complete oscillation?

ib-hl-hmcq-2-ans-options

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    3
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    Which equation correctly shows the kinetic energy-displacement relation for simple harmonic motion?

    • K subscript E space equals space 1 half m v squared

    • E subscript T equals space 1 half m omega squared x subscript 0 squared

    • E subscript P space equals space 1 half k increment x squared

    • E subscript K space equals space 1 half m omega squared open parentheses x subscript 0 squared space minus space x squared close parentheses

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    4
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    The defining equation of SHM describes the relationship between acceleration, a, angular frequency, ω, and displacement, x, from the equilibrium position:

     a space equals space minus omega squared x

    Which value correctly shows the resulting acceleration if the angular frequency was doubled?

    • negative 4 a

    • 1 fourth a

    • 2 a

    • 4 a

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    5
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    The graph shows the displacement over time of a simple pendulum oscillating in simple harmonic motion. 

    ib-hl-emcq-5-q-stem

    What is the potential energy of the pendulum at points X, Y and Z?

     

     

    X

    Y

    Z

    A.

    Max

    Zero

    Max

    B.

    Zero

    Max

    Zero

    C.

    		 Max Max Zero

    D.

    		 Zero

    Zero

    Max

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      6
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      A spring loaded with mass m oscillates with simple harmonic motion. The amplitude of the motion is A and the spring has total energy E.

      What is the total energy of the spring when both the mass and the amplitude are doubled?

      • E T

      • 2E T

      • 4E T

      • 8E T

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      7
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      A simple pendulum undergoes simple harmonic motion. The kinetic energy of the pendulum is at a maximum at the equilibrium position.

      How many times during one oscillation is the kinetic energy of the pendulum equal to its gravitational potential energy?

      • 1

      • 2

      • 3

      • 4

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      8
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      A mass with mass, m, is attached to a spring with a spring constant, k, and oscillates in simple harmonic motion with a period, T. 

      A new spring is introduced with a spring constant of 4k. How does this affect the period of the oscillation?

      • 1 fourth T

      • 1 half T

      • 2 T

      • 4 T

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      9
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      A particle oscillates in simple harmonic motion. The particle's displacement over time is shown in the following graph.

      ib-hl-emcq-q10-stem

      Which graphs are the correct velocity-time and acceleration-time graphs for this particle?

       

      b-hl-emcq-q10-options

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        1
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        A point on a guitar string S oscillates about its equilibrium position Z in simple harmonic motion.

        9-1-hl-mcq-medium-1-diagram

        The amplitude of the oscillation is YZ.

        Which positions show when the acceleration of point S is at a maximum and the velocity of point S is at zero?

         

        Acceleration

        Velocity

        A.

        Z

        Y

        B.

        Y

        Y

        C.

        		 Z Z

        D.

        		 Y

        Z

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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 the oscillations is T. The pendulum and the mass-spring system are taken to Mars where the acceleration of free fall is smaller than on Earth.

          Which answer 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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            Choose the correct statement describing the quantities that remain constant for an object in SHM.

            • Frequency, f.

            • Frequency, f, & period, T.

            • Period, T, & the spring constant, k.

            • Period, T, frequency, f, spring constant, k, & acceleration of freefall, g.

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            4
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            A mass-spring system oscillates with simple harmonic motion. The mass m has an amplitude A and the spring has a total energy E. The mass is increased by half and the amplitude increased to 4A.

            What is the total energy in the spring?

            • 24E

            • 12E

            • 8E

            • 6E

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            5
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            A pendulum oscillating with simple harmonic motion has an amplitude x subscript 0 and a maximum kinetic energy Ek.

            What is the potential energy of the system when the pendulum bob is at a distance 0.4x subscript 0 from its maximum displacement?

            • 0.36Ek

            • 0.4Ek

            • 0.6Ek

            • 0.64Ek

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            6
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            Which of the following is a correct arrangement for the maximum displacement of a particle performing simple harmonic motion?

            • x subscript 0 = −fraction numerator a subscript m a x end subscript space f squared over denominator 4 straight pi squared end fraction

            • x subscript 0 = −fraction numerator a subscript m a x end subscript over denominator 2 straight pi f squared end fraction

            • x subscript 0 = −fraction numerator a subscript m a x end subscript over denominator 4 straight pi squared T squared end fraction

            • x subscript 0 = −fraction numerator a subscript m a x end subscript T squared over denominator 4 straight pi squared end fraction

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            7
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            An ion in a crystal lattice structure oscillates with simple harmonic motion. The period of the oscillation is T. T is measured from equilibrium.

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

            9-1-hl-mcq-medium-m7-question-stem

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              8
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              A simple pendulum performs simple harmonic motion. The pendulum bob has a mass m, the string has a length l, and the pendulum has a period T. 

              Which is the correct value for the period T if the mass of the pendulum bob is doubled and the length of the string is halved?

              • 1.4 T

              • 0.7 T

              • 0.5 T

              • 0.25 T

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              9
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              A mass-spring system oscillates about its equilibrium position in simple harmonic motion. A bulb on the motion sensor lights up each time the block passes the equilibrium position.

              9-1-hl-mcq-m9-question-stem

              The block has a mass m and oscillates with a period T. 

              Select the new mass that would cause the period to double.

              • 0.5m

              • 1.4m

              • 2m

              • 4m

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              10
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              A simple pendulum oscillates with simple harmonic motion as shown.

              9-1-hl-mcq-medium-m10-question-stem

              At which positions are the acceleration at zero, the displacement at a negative maximum, and velocity at a maximum?

               

              Acceleration

              Displacement

              Velocity

              A.

              Z

              Y

              X

              B.

              Y

              X

              Y

              C.

              		 X Z Z

              D.

              		 Y

              X

              Z

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                1
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                The following graph shows the acceleration as a function of time for a simple pendulum oscillating isochronously. 

                gz4QtOVG_9-1-ib-hl-hmcq-2-q-stem

                Which of the following gives the times at which kinetic energy is at a maximum?

                • T over 2 comma space T

                • T over 4 comma space fraction numerator 3 T over denominator 2 end fraction

                • T over 4 comma space T over 2

                • fraction numerator 3 T over denominator 2 end fraction comma space T

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                2
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                A mass-spring system is set up horizontally on a frictionless surface. The spring is extended to the left and released so that the mass oscillates in SHM.

                Taking motion to the left to be positive, which of the following statements is correct about the motion of the mass?

                • At fraction numerator 3 T over denominator 2 end fraction, velocity = − maximum

                • At T over 2, acceleration = − maximum

                • At T over 4, Potential Energy = maximum

                • At T, Acceleration = − maximum

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                3
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                An object oscillates about its equilibrium position periodically. It has a total energy E and period T. The amplitude is reduced to one quarter of the original amplitude.

                What is the new total energy and period of the system?

                 

                 

                Total energy

                Period

                A.

                E over 16

                T over 4

                B.

                E over 8

                T over 2

                C.

                		 E over 16 T

                D.

                		 E over 4

                4 T

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                  4
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                  A simple pendulum oscillates with a time period T near the surface of the Earth. The same pendulum is moved to the surface of the Moon where the acceleration of free fall is 0.2 g.

                  What is the best estimate for the value of T for the pendulum near the surface of the moon?

                  • 0.2 T

                  • 0.4 T

                  • 1.4 T

                  • 2.2 T

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                  5
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                  A body of mass 0.40 kg is subjected to a force F which varies with its displacement x from a fixed point as shown in the graph below.

                  xiderTJz_9-1-ib-hl-hmcq-7-q-stem

                  What is the maximum velocity of the body?

                  • 1.6 m s−1

                  • 2.2 m s−1

                  • 2.8 m s−1

                  • 3.4 m s−1

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                  6
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                  A satellite rotates clockwise around a planet of radius r with an angular velocity ω. The satellite passes position S at time zero and position P at time t. Q is the projection of P onto the diameter through S. Measured with respect to the origin O, the displacement, linear velocity and linear acceleration of Q in the direction OS are x, v, and a respectively. 

                  c~VCxHMW_9-1-ib-hl-hmcq-8-q-stem

                  A.

                  x space equals space r cos omega t

                  v space equals space minus r omega sin omega t

                  a space equals space r omega squared cos omega t

                  B.

                  x space equals space r cos omega t

                  v space equals space minus r omega sin omega t

                  a space equals space minus r omega squared cos omega t

                  C.

                  		 x space equals space r sin omega t v space equals space minus r omega cos omega t a space equals space r omega squared sin omega t

                  D.

                  		 x space equals space r sin omega t

                  v space equals space minus r omega cos omega t

                  a space equals negative space r omega squared sin omega t

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                    7
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                    A small ball bearing oscillates in simple harmonic motion. 

                    OQyZe_nn_9-1-ib-hl-hmcq-9-q-stem

                    Which is a correct expression for the kinetic energy per unit mass of the ball bearing?

                    • fraction numerator straight pi squared h squared over denominator 2 T squared end fraction

                    • fraction numerator h straight pi over denominator T squared end fraction

                    • fraction numerator h squared straight pi over denominator 2 T end fraction

                    • fraction numerator straight pi squared h squared over denominator T squared end fraction

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                    8
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                    The table below shows the values for the acceleration and displacement of a particle moving isochronously.

                     

                    a (mm s−2)

                    16

                    8

                    0

                    − 8

                    − 16

                    x (mm)

                    − 4

                    − 2

                    0

                    2

                    4

                     

                    What is the period of the motion?

                    • 2 over straight pis

                    • straight pi s

                    • 2 straight pi s

                    • straight pi squared s

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                    9
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                    A pendulum bob is suspended by a thread. The bob is moved to the right and released so that the pendulum oscillates isochronously. 

                    Taking motion to the left to be positive, which of the following statements is incorrect about the motion of the pendulum?

                    • The potential energy of the system will reach its maximum value three times in one oscillation

                    • At T over 4 the kinetic energy of the system is at its maximum value and the velocity is maximum in the positive direction

                    • At fraction numerator 3 T over denominator 4 end fraction the kinetic energy of the system is at a maximum and the velocity is at a maximum in the negative direction

                    • At T over 2, the force is acting in the negative direction and the kinetic energy is at its maximum value

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