simple harmonic motion mc packet (final) - …whphysics.com/oscillationsmcpracticequestions.pdf ·...

Simple Harmonic Motion MC Question Database

1) Which of the following are characteristics of simple harmonic motion? Select two answers.

(a) The acceleration is constant. (b) The restoring force is proportional to the displacement. (c) The frequency is independent of the amplitude. (d) The period is dependent on the amplitude. Multi-select: For questions 30-34, two of the suggested answers will be correct. Select the two best answers.

2) Which of the following are not examples of simple harmonic motion?

a) A tennis ball bouncing on the ground b) A child swinging freely back and forth in a toddler swing c) A plucked guitar string d) A child who continues to jump up and down e) A ball rolling back and forth in a bowl 3) Which of the following best represent periodic motion?

a) A skydiver who has reached terminal velocity b) The Moon in orbit about the Earth c) A car driving to each state in the United States d) A cart pushed up a frictionless incline plane e) A pendulum swinging over a 30-min time span


4) A mass of 12 kg is hung onto a spring attached to the ceiling. The spring’s constant is 19 N/m. How far will the spring stretch when the weight is hung, and what will be the system’s period when activated? a) 6.2 cm and 15 s b) 6.2 m and 5 min c) 62 mm and 15.6 s d) 6.2 m and 5 s e) 6.2 m and 156 s 5) A spring with a constant of 300 N/m is stretched by 0.5 m. What is the force on the spring?

a) 50 N b) 100 N c) 150 N d) 200 N e) 300 N


6) A spring with stiffness constant k = 50 N/m has a natural length of 0.45 m. It is attached to the top of an incline that makes a 30° angle with the horizontal. The incline is 2.4 m long. A mass of 2 kg is attached to the spring, causing it to be stretched down the incline. How far down the incline does the end of the spring rest?

a) 0.196 m b) 0.45 m c) 0.646 m d) 0.835 m e) 1.2 m


7) A body of mass m, attached to an ideal spring whose spring constant is k, is set into motion on a horizontal frictionless surface with an amplitude of vibration of A. Which of the following statements is correct? (a) Increasing the amplitude of vibration by a factor of 2 will increase the period of vibration since the mass has to travel a greater distance in making a complete vibration. (b) Increasing the spring constant by a factor of 2 will keep the amplitude the same, but will change the period of the motion by a factor of √2. (c) Increasing the spring constant by a factor of 2 will increase the amplitude by a factor of √2 but will not change the period. (d) Increasing the spring constant by a factor of 2 will increase both the amplitude and period of motion by a factor of √2.


8) When a 0.05 kg mass is attached to a vertical string, it is observed that the spring stretches 0.03 m. The system is then placed horizontally on a frictionless surface and set into simple harmonic motion. What is the period of the oscillations? (a) 0.75 s (b) 0.12 s (c) 0.35 s (d) 1.3 s (e) 2.3 s 9) A mass of 50 kg is held horizontally on a frictionless surface by two springs, one at each end of the mass. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period? a) 14.04962946 s b) 7.024814731 s c) 14 s d) 7 s e) 0.14 s


10) A mass of 50 kg is held horizontally on a frictionless surface by two springs, one connected to the other in series. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period? a) 0.14 s b) 14 s c) 7 s d) 14.04962946 s e) 7.024814731 s 11) A 10-kg mass is placed on a frictionless surface and attached to a spring that is attached to a fixed wall. The spring’s constant is 20 N/m. When set in motion, what is the system’s period, and what is the period if the system is held vertically? a) 4.4 s and 8.9 s b) 8.885765876 s for both c) 8.885765876 s and 17.77153175 s d) 4.4 s for both e) 13 s for both


12) A spring-block simple harmonic oscillator is set up so that the oscillations are vertical. The period of the motion is T. If the spring and the block are taken to the surface of the Moon, where the gravitational acceleration is 1/6 of its value here, then the vertical oscillations will have a period of

(a) T/6 (b) T/3 (c) T/√6 (d) T 13) A spring-mass system with parameters m and k is oscillating vertically. A second spring-mass system with 3 times the mass is set up beside the first. If the two systems are to oscillate in unison, the spring constant of the second system must be a) 3k b) k/3 c) √3 k d) k/√3 e) 9k


14) A spring supported vertically from a clamp is elongated 0.100 m when a 0.200 kg body is hung from the free end. If this mass is replaced by a 0.400 kg body and set into simple harmonic motion, SHM, what is the period of vibration?

(a) 0.634 s (b) 0.897 s (c) 1.10 s (d) 1.58 s 15) One end of a 50-kg mass is attached to two vertical springs in parallel. Each spring has a spring constant of 20 N/m. When the spring is pulled back and released, what is the system’s period? a) 14.04962946 s b) 7.024814731 s c) 14 s d) 7 s e) 0.14 s


16) A mass of 50 kg is held vertically by two springs, one connected to the other in series. Each spring has a spring constant of 20 N/m. When set in motion, what is the system’s period? a) 0.14 s b) 14 s c) 7 s d) 14.04962946 s e) 7.024814731 s 17) A 15-kg mass rests on two springs and is held by a spring attached to the ceiling. The spring constant for each of the bottom two springs is 10 N/m, and the spring constant for the upper spring is 25 N/m. When set in motion, what is the system’s period? a) 3.6 s b) 7.2 s c) 1.8 s d) 1.2 s e) The mass will not move.


18) The Moon is approximately 384,000 km from the Earth. The Moon revolves around the Earth once every 27.3 days. What is the frequency of the Moon’s rotation? a) 14,100 km each day b) 0.0366 revolution each day c) 0.036630 revolution each day d) 655 hours per revolution e) 27.3 days per revolution 19) A wave generator in a pool produces one wave every minute. What is the frequency of vibration?

a) 60 s b) 1 Hz c) 0.02 Hz d) 60 Hz e) 1 s


20) A refrigerator compressor that weighs 8 kg is fixed to 3 separate springs on the refrigerator frame. Each has a spring constant of 0.01 N/m. What is the natural frequency of the system?

a) 0.01 cycle/s b) 0.03 cycle/s c) 0.8 cycle/s d) 103 cycles/s e) 0.003 cycle/s 21) The mass is suspended from a vertical spring attached to a support. Which of the following significantly affect the frequency of oscillation of this system?

a) The spring constant b) The gravitational field strength c) The value of the mass d) Friction between the mass and the spring e) The surface area of the mass


22) A mass oscillates from the end of a vertical spring. What may be done to increase the frequency of oscillation?

a) Increase the mass b) Decrease the mass c) Increase the spring constant d) Increase the strength of the gravitational field e) Increase the amplitude of vibration 23) A mass is suspended from a spring and allowed to oscillate freely. When the amplitude of vibrations is doubled, what happens to the frequency of vibrations?

a) It quadruples. b) It doubles. c) It stays the same. d) It reduces to one-half of what it was. e) It reduces to one-fourth of what it was.


24) A linear spring of force constant k is used in a physics lab experiment. A block of mass m is attached to the spring and the resulting frequency, f, of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If f2 is plotted versus 1/m, the graph will be a straight line with a slope

(a) 4π2/k2 (b) 4π2/k (c) 4π2k (d) k/4π2


25) A mass is attached to a spring and allowed to oscillate vertically. Which of the following would not change its period of oscillation? a) double the mass and double the spring constant b) double the amplitude of vibration and double the mass c) double the gravitational field strength and double the mass d) double the gravitational field strength and double the spring constant e) double the gravitational field strength and quadruple the mass 26) A particle oscillates with simple harmonic motion with no damping. Which one of the following statements about the acceleration of the oscillating particle is true? a) It has a value of 9.8 m/s2 when the oscillation is vertical. b) It is zero when the speed is the minimum. c) It is proportional to the frequency. d) It is zero throughout the oscillation. e) It is zero when the speed is the maximum.


27) A 0.300 kg block attached to a spring moves on a flat frictionless surface under the action of an elastic restoring force. The spring constant for the spring is 25.0 N/m. Which of the following statements is correct?

(a) The force acting on the spring is proportional to the displacement of the spring and is directed to the equilibrium position; therefore, the acceleration is variable and points to the equilibrium position as the displacement changes.

(b) The force acting on the spring is inversely proportional to the displacement of the spring and is directed to the equilibrium position; therefore, the acceleration is variable and points to the equilibrium position.

(c) The force is constant; the block moves with constant acceleration in the direction of the elastic restoring force.

(d) Since the force points to the equilibrium and is proportional to the displacement, the magnitude of the acceleration is variable, but will point toward the maximum displacement.


28) A 0.4-kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillates with a constant amplitude of 12 cm. What is the maximum acceleration of the system? a) 0.62 m/s2 b) 1.4 m/s2 c) 1.6 m/s2 d) 3.6 m/s2 e) 9.8 m/s2


Questions 29 and 30 are based on the figure below of a mass-spring system. Assume the mass is pulled back to position +A and released, and it slides back and forth without friction.

29) When the mass reaches position –A, what can be said about its speed?

a) It is a minimum. b) It is a maximum. c) It is zero. d) It is decreasing. e) It is increasing.

30) When the mass reaches position 0, what can be said about its speed?

a) It is a minimum. b) It is a maximum. c) It is zero. d) It is decreasing. e) It is increasing.


31) A block of mass m = 0.250 kg is attached to a spring, k = 20.0 N/m and is undergoing simple harmonic motion (SHM) on a frictionless surface. The mass oscillates under the action of an elastic restoring force. Determine the acceleration of the mass when its displacement is -0.150 m.

(a) 12 m/s2 (b) -12 m/s2 (c) 5 m/s2 (d) -5 m/s2 32) At what position does the mass have the greatest acceleration? (Consider acceleration in the positive direction to be greater than acceleration in the negative direction).

a) -A b) –A/2 c) 0 d) +A/2 e) +A


33) The mass is released from the –A position at time t = 0, and it oscillates with period T, measured in seconds. Which equation best represents the displacement?

a) Δx = -A cos(Tt/2π) b) Δx = -(A/2) cos(2πTt) c) Δx = -A cos(2πt/T) d) Δx = (A/2) cos(Tt) e) Δx = A cos(2πt/T) 34) The displacement (in centimeters) of the vibrating cone of a large loudspeaker is represented by the equation Δx = 2cos(150t), where t is the time in seconds. What distance does the tip of the cone move in half a period? a) 0.007 cm b) 1.0 cm c) 2.0 cm d) 4.0 cm e) 150 cm


35) The graph shows the displacement versus time for an object. Which equation best describes its displacement in meters?

a) Δx = 20 cos(0.5t) b) Δx = 10 cos(2t) c) Δx = 10 cos(πt) d) Δx = 20 cos(2t) e) Δx = 20 sin(πt)


36) The displacement (in centimeters) of the vibrating cone of a large loudspeaker is represented by the equation Δx = 2cos(150t). What is the frequency of the vibration of the tip of the cone? a) 24 Hz b) 0.042 Hz c) 150 Hz d) 2.0 Hz e) 1.0 Hz


37) The simple harmonic motion of a 0.200 kg mass oscillating on a spring of constant k is shown in the graph below.

What is the value of the spring constant in N/m? (a) 4/π (b) π2/2 (c) 8/π2 (d) π2/4


38) A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where

(a) the speed is maximum (b) the speed is minimum (c) the restoring force is minimum (d) the restoring force is maximum 39) A mass M is attached to a spring on a frictionless, horizontal surface and set into oscillation. A smaller mass sits on top of the first and moves with it without slipping. The static friction force exerted on the smaller mass a) is equal to µsN throughout the motion b) reaches a maximum value as the masses reach their maximum speed c) reaches a maximum value as the masses reach their minimum speed d) reaches a maximum value at a point where the speed is between its maximum and minimum values e) remains constant but is less than µsN


40) Which choice below best explains why a pendulum does not oscillate in zero gravity?

a) The pendulum has no mass in zero gravity. b) A pendulum requires gravity to create the restoring force. c) The pendulum is in orbit and considered weightless. d) The pendulum would be too far from the Earth to work properly. e) The pendulum must have an oscillating tension in the string to function properly. 41) A pendulum has a bob of 28 kg and is 38 cm in diameter. It is hung on a wire that is 67 m long. What are its period and frequency near the surface of the Earth? a) 0.061 s and 16 cycles/s b) 16 s and 0.061 cycles/s c) 0.060869 s and 16.429 cycles/s d) 11 s and 0.0 94 cycles/s e) 0.094 s and 11 cycles/s


42) The pendulum on an old mechanical, weight-driven clock has period of 3 s. What is the length of the clock’s pendulum? a) 2.2 m b) 3.5 m c) 22 cm d) 35 cm e) 3 m 43) A pendulum on the surface of the Moon has a period of 1 s. If the length of the pendulum is quadrupled, what is the value of the new period?

a) 0.25 s b) 0.50 s c) 1.0 s d) 2.0 s e) 4.0 s


44) A 2-m pendulum on a particular planet has a period of 4.6 s. What is the gravitational field strength on that planet?

a) 1.6 N/kg b) 3.7 N/kg c) 4.9 N/kg d) 9.8 N/kg e) 25 N/kg 45) The Moon has a gravitational field strength that is approximately one-sixth of the field on the Earth. What is the ratio between the period of a pendulum on the Moon and the period of an identical pendulum on the Earth?

a) 6 b) √6 c) 1/6 d) 1/√6 e) 1


46) Which of the following significantly affect the period of a pendulum?

a) The length of the pendulum b) The mass of the pendulum bob c) The amplitude of swing d) The gravitational field strength e) The thickness of the string 47) What is the length of a pendulum whose period, at the Equator, is 1 s?

a) 0.15 m b) 0.25 m c) 0.30 m d) 0.45 m e) 1.0 m 48) If the length of a simple pendulum is doubled, its period will

(a) decrease by 2 (b) increase by 2 (c) decrease by √2 (d) increase by √2 (e) remains the same


49) The pendulums of two grandfather clocks have the same length. One clock (A) runs faster than the other clock (B). Which of the following statements is true?

(a) Pendulum A is more massive. (b) Pendulum B is more massive. (c) Pendulum A swings through a smaller arc. (d) Pendulum B swings through a smaller arc. (e) None of the above statements is true. 50) A bell is rung when the dangling clapper within it makes contact with the bell. A poorly designed bell has a clapper that swing with the same frequency as the bell. How can this design be improved? a) Use a clapper with a smaller mass on the end so it is out of period with the bell. b) Use a clapper with a bigger mass on the end so it is out of period with the bell. c) Force the bell to swing with greater amplitude. d) Use a longer clapper so it is out of period with the bell. e) Increase the mass of the bell so it makes better contact with the clapper.


51) Several simple pendulums are shown in the diagram below. Each pendulum is set in motion by releasing the masses from the same angle with the vertical.

Rank the pendulums from the pendulum having the highest frequency to the one with the lowest frequency.

(a) A > B > C > D (b) A > C > D > B (c) B > A > D > C (d) B > D > A > C

52) A simple pendulum of mass m and length L on the surface of the Earth oscillates with a period T. The pendulum is moved to a location a distance RE above the surface of the Earth and replaced with a mass of 2m while keeping its length as L. Its new period is

(a) T2 = T1 (b) T2 = √2T1 (c) T2 = 2 T1 (d) T2 = 4T1


53) Several students perform an experiment using a 0.150 kg pendulum bob attached to a string and obtain the following data:

They want to determine an experimental value for the acceleration due to the gravitational force in the classroom using the information from the slope of the line. In order to do this, they should plot the data using which of the graphs below?

(a) I (b) II (c) III (d) IV


54) An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring, also with period T. If the masses of both objects are doubled, what are the new values for the periods?

Pendulum Mass on the Spring

(a) T/√2 T√2 (b) T T√2 (c) T√2 T/√2 (d) T T 55) A simple pendulum swing about the vertical equilibrium position with a maximum angular displacement of 5 degrees and period T. If the same pendulum is given a maximum angular displacement of 10 degrees, then which of the following best gives the period of the oscillations?

(a) T/2 (b) T/√2 (c) T (d) 2T


56) To increase the period of a simple pendulum by a factor of two, you could I. double the mass II. double the length III. quadruple the length a) I only b) II only c) III only d) I and II only e) I and III only 57) A given pendulum on Earth has a period T. On the Moon, where the acceleration due to gravity is 1/6 that of Earth, the period will be a) T/6 b) T c) √6 T d) T/6 e) T/√6


58) A pendulum consists of a rope of length 2 m and a bob of mass 4 kg. It moves through its lowest point with a speed of 6 m/s. The tension in the rope is most nearly a) 40 N b) 72 N c) 32 N d) 112 N e) 48 N 59) A pendulum bob is attached to a string that is tied to the ceiling, and the bob is pulled back and released. As the bob moves through the bottom of the swing, how does the magnitude of the tension force from the string compare to the gravitational force on the bob? a) The tension force is less than the gravitational force. b) The tension force is greater than the gravitational force. c) The tension force is equal to the gravitational force. d) The mass of the ball is needed in order to compare these forces. e) The release height of the ball is needed in order to compare these forces.


60) A pendulum bob is attached to a string that is tied to the ceiling, and the bob is pulled back and released. As the bob moves through the bottom of the swing, how is its centripetal acceleration related to its speed? a) The centripetal acceleration is directly proportional to the speed of the pendulum. b) The centripetal acceleration is inversely proportional to the speed of the pendulum. c) The centripetal acceleration is directly proportional to the square of the speed of the pendulum. d) The centripetal acceleration is inversely proportional to the square of the speed of the pendulum. e) There is no relationship between the centripetal acceleration and the speed.

simple harmonic motion mc packet (final) - …whphysics.com/oscillationsmcpracticequestions.pdf ·...

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