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1. Characteristics of simple harmonic motion include which of the following?
I. The acceleration is constant.
II. The restoring force is proportional to the displacement.
III. The frequency is independent of the amplitude.
A. II onlyB. I and II onlyC. I and III onlyD. II and III onlyE. I, II, and III
2. 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 the maximumB. the potential energy is the minimumC. the speed is the minimumD. the restoring force is the minimumE. the kinetic energy is the maximum
3. A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x = 0) with amplitude A. What fraction of the total energy is in the form of kinetic energy when the block is at position x = A ?
A. B. C. D. E.
4. A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude A on the end of an ideal spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will
A. decrease by a factor of 4B. decrease by a factor of 2C. decrease by a factor of D. remain the sameE. increase by a factor of 2
5. 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 block are taken to the surface of the moon, where the gravitational acceleration is of its value here, then the vertical oscillations will have a period of
A. B. C. D. TE. T
6. 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 slope
A. 4π2/k2B. 4π2/kC. 4π2kD. k/(4π2)E. k2/(4π2)
7. A block of mass m = 4 kg on a frictionless, horizontal table is attached to one end of a spring of force constant k = 400 N/m and undergoes simple harmonic oscillations about its equilibrium position (x = 0) with amplitude A = 6 cm. If the block is at x = 6 cm at time t = 0, then which of the following equations (with x in centimeters and t in seconds) gives the block’s position as a function of time?
A. x = 6 sin(10t + π)B. x = 6 sin(10πt)C. x = 6 sin(10πt – π)D. x = 6 sin(10t)E. x = 6 sin(10t –π)
8. A student is performing a lab experiment on simple harmonic motion. She has two different springs (with force constants k1 and k2) and two different blocks (of masses m1 and m2). If k1 = 2k2 and m1 = 2m2, which of the following combinations would give the student the spring–block simple harmonic oscillator with the shortest period?
A. The spring with force constant k1 and the block of mass m1B. The spring with force constant k1 and the block of mass m2C. The spring with force constant k2 and the block of mass m1D. The spring with force constant k2 and the block of mass m2E. All the combinations above would give the same period.
9. A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5 and period T. If the same pendulum is given a maximum angular displacement of 10°, then which of the following best gives the period of the oscillations?
A. B. C. TD. TE. 2T
10. A simple pendulum of length L and mass m aswings about the vertical equilibrium position (θ = 0) with a maximum angular displacement of θmax. What is the tension in the connecting rod when the pendulum’s angular displacement is θ = θmax ?
A. mg sinθmaxB. mg cosθmaxC. mgL sinθmaxD. mgL cosθmaxE. mgL(1 – cosθmax)
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