Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.) A) The period is doubled. B) The angular frequency is doubled. C) The amplitude is doubled. D) The period is reduced to one-half of what it was. E) The angular frequency is reduced to one-half of what it was. Answer: B, D 2) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a function of time? A) graph a B) graph b C) graph c D) graph d Answer: B 3) In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.) A) when the speed is a maximum B) when the displacement is a zero 1 Copyright © 2014 Pearson Education, Inc. C) when the magnitude of the displacement is a maximum D) when the potential energy is a maximum E) when the kinetic energy is a minimum Answer: C, D, E 4) An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could A) double the amplitude of vibration. B) double the force constant (spring constant) of the spring. C) double both the amplitude and force constant (spring constant). D) double the mass. E) double both the mass and amplitude of vibration. Answer: B 5) A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its acceleration is zero. B) Its speed is zero. C) Its elastic potential energy is zero. D) Its kinetic energy is a maximum. E) Its total mechanical energy is zero. Answer: A, C, D 6) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: A 7) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: B 8) Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B? A) T/ B) T C) T 2 Copyright © 2014 Pearson Education, Inc. D) 2T E) T/2 Answer: B 9) Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.) A) Both systems will have the same period on the Moon as on Earth. B) On the Moon, ball A will take longer to complete one cycle than ball B. C) On the Moon, ball B will take longer to complete one cycle than ball A. D) On the Moon, ball A will execute more vibrations each minute than ball B. E) On the Moon, ball B will execute more vibrations each minute than ball A. Answer: C, D 10) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Raise the weight. B) Lower the weight. C) Add more mass to the weight. D) Remove some mass from the weight. E) Decrease the amplitude of swing by a small amount. Answer: B 11) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration? A) The period does not change. B) The period increases. C) The period decreases. D) The period becomes zero. E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. Answer: B 12) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall? A) The period does not change. B) The period increases slightly. C) The period decreases slightly. D) The period becomes zero. E) The period becomes infinite because the pendulum would not swing. Answer: E 3 Copyright © 2014 Pearson Education, Inc. 13) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems? A) Both periods would remain the same. B) Both periods would increase. C) Both periods would decrease. D) The period of the pendulum would increase but the period of the spring would stay the same. E) The period of the pendulum would decrease but the period of the spring would stay the same. Answer: A 14) A leaky faucet drips 40 times in A) 1.3 Hz B) 0.75 Hz C) 1.6 Hz D) 0.63 Hz Answer: A What is the frequency of the dripping? 15) If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz? A) 4560 Hz B) 1450 Hz C) 3.98 Hz D) 2.54 Hz E) 1.27 Hz Answer: E 16) If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change? A) 4 B) 2 C) D) 2/π Answer: A 17) The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm? A) 4.34 s B) 0.108 s C) 0.129 s D) 7.39 s E) 7.75 s Answer: C 18) An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s? 4 Copyright © 2014 Pearson Education, Inc. A) 1.33 cm/s2 B) 0.784 cm/s2 C) 11.5 cm/s2 D) 14.9 cm/s2 E) 0.00 cm/s2 Answer: D 19) If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4 Answer: A 20) A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring? A) 2.45 N/m B) 12.1 N/m C) 24.1 N/m D) 0.102 N/m E) 0.610 N/m Answer: C 21) When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations? A) 0.695 s B) 0.483 s C) 0.286 s D) 0.0769 s E) 1.44 s Answer: A 22) A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is its kinetic energy is closest to A) 0.90 J. B) 0.84 J. C) 0.95 J. D) 1.0 J. E) 1.1 J. Answer: A 5 Copyright © 2014 Pearson Education, Inc. 23) How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz? A) 39.5 kg B) 2.00 kg C) 1.00 kg D) 1.56 kg E) 6.29 kg Answer: C 24) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same? A) 0.017 m B) 0.029 m C) 0.12 m D) 0.17 m Answer: D 25) A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position? A) 0.00 J B) 0.22 J C) 0.45 J D) 0.90 J E) 1.4 J Answer: A 26) A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables. A) 4.4 s B) 4.8 s C) 5.3 s D) 5.7 s Answer: A 27) On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? A) T B) T/ C) T/6 D) 6T E) T/3 6 Copyright © 2014 Pearson Education, Inc. Answer: A 28) A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period? A) 2T B) T C) T D) T/ E) T/2 Answer: C 29) A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing? A) 6.00 s B) 3.46 s C) 2.00 s D) 1.15 s E) 0.667 s Answer: B 30) An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N40? A) 4.85 m/s2 B) 1.66 m/s2 C) 3.74 m/s2 D) 2.39 m/s2 E) 9.81 m/s2 Answer: C Free response 1) If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave? Answer: 0.25 Hz, 4.0 s 2) A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b) How long does it take the needle tip to travel a total distance of 11.43 cm? Answer: (a) 0.20 s (b) 0.90 s 3) A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. 7 Copyright © 2014 Pearson Education, Inc. (a) What is the maximum speed of that point in SI units? (b) What is the maximum acceleration of the point in SI units? Answer: (a) 6.82 m/s (b) 3.75 × 104 m/s2 4) A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time t, if x is equal to 8.3 cm at t = 0.0 s. Use the cosine function. Answer: x = (8.3 cm) cos[2πt/(4.6 s)] or x = (8.3 cm) cos[(1.4 s-1)t] 5) An object oscillates such that its position x as a function of time t obeys the equation x = (0.222 m) sin(314 s-1 t), where t is in seconds. (a) In one period, what total distance does the object move? (b) What is the frequency of the motion? (c) What is the position of the object when t = 1.00 s? Answer: (a) 0.888 m (b) 50.0 Hz (c) -0.0352 m 6) When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (spring constant) of 467 N/m, the system obeys the equation y = (4.4 cm) cos(33.3 s-1 t). What is the mass of this laboratory sample? Answer: 0.421 kg 7) An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant) 1720 N/m. The object is set into simple harmonic motion, with an initial velocity of and an initial displacement of Calculate the maximum speed the object raches during its motion. Answer: 4.5 m/s 8) A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what distance from the equilibrium position are the kinetic energy and the potential energy the same? Answer: (a) 0.24 m (b) 0.17 m 9) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system? Answer: (a) 0.56 J (b) 0.24 m 10) As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is (Assume that once the pendulum ball hits the spring there is 8 Copyright © 2014 Pearson Education, Inc. no effect due to the vertical movement of the ball.) Answer: 3.0 s 9 Copyright © 2014 Pearson Education, Inc.

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