Page 191 - Schaum's Outline of Theory and Problems of Applied Physics

176 SIMPLE HARMONIC MOTION [CHAP. 14

14.7. A 200-lb portable gasoline-powered generating set is placed on four springs, which are depressed by 0.5 in. What
is the natural frequency of vibration of this system?

14.8. A spring has a 0.3-s period of oscillation when a 30-N weight is suspended from it. By how much will the spring
stretch when a 50-N weight replaces the 30-N weight?

14.9. A hammer suspended from a spring whose force constant is 180 N/m oscillates up and down 120 times per minute.
What is the mass of the hammer?
14.10. A shaking table used to study the effects of accelerations on electronic equipment undergoes simple harmonic motion
with an amplitude of 20 mm. At what frequency will the maximum acceleration equal 10g?
14.11. An object is oscillating in simple harmonic motion with an amplitude of 1 cm and a period of 0.2 s. Find the
magnitudes of its velocity and acceleration when its displacement from the equilibrium position is 0.3 cm.
14.12. Find the total energy of the oscillator of Prob. 14.11.

14.13. The piston of a refrigeration compressor weighs 1 lb and has a stroke of 3 in. When the compressor is operated at
600 rev/min, find the piston’s maximum velocity and acceleration and the maximum force acting on it.
14.14. Find the frequency of a simple pendulum 20 cm long.

14.15. What is the length in inches of a simple pendulum whose period is 1 s?

14.16. A pendulum 1.00 m long oscillates 30.0 times per minute in a certain location. What is the value of g there?

14.17. The prongs of a tuning fork vibrate at 440 Hz (the musical note A) with an amplitude of 0.5 mm at the tips. Find the
maximum velocity of the tips.

14.18. A uniform steel girder 20 ft long is suspended from one end. What is the period of its oscillations?
14.19. A 24-kg wooden sphere whose diameter is 40 cm is suspended by a wire. A torque of 0.5 N·m is found to rotate the
sphere through 10 . Find the period of oscillation of the sphere.
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14.20. A disk whose moment of inertia is 0.5 kg·m is suspended by a thin rod. When the disk is turned through a few
degrees and then released, it oscillates back and forth twice per second. Find the torsion constant of the rod.

Answers to Multiple-Choice Questions

14.1. (d) 14.8. (b)

14.2. (b) 14.9. (d)
14.3. (c) 14.10. (a)

14.4. (c) 14.11. (d)

14.5. (d) 14.12. (c)

14.6. (c) 14.13. (b)

14.7. (c)