Page 190 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 14] SIMPLE HARMONIC MOTION 175

14.7. If it is pressed down and released, the mass of Question 14.5 will oscillate up and down with a period of
(a) 0.0032 s (c) 0.14 s
(b) 0.057 s (d) 0.44 s

14.8. A particle that undergoes simple harmonic motion has a period of 0.40 s and an amplitude of 12 mm. The maximum
velocity of the particle is
(a) 3 cm/s (c) 38 cm/s
(b) 19 cm/s (d) 43 cm/s

14.9. If a mass of 15 g is to oscillate at 12 Hz, it should hang from a spring whose force constant is
(a) 1.1 N/m (c) 7.1 N/m
(b) 1.3 N/m (d) 85 N/m

14.10. The end of a diving board moves down by 30 cm when a girl stands on it. If she then bounces up and down, the
frequency of the oscillations
(a) is 0.91 Hz (c) is 2.3 Hz
(b) is 1.1 Hz (d) depends on her mass

14.11. To increase the period of a harmonic oscillator from 3 to 6 s, its original mass of 20 g should be changed to
(a) 5 g (c) 40 g
(b) 10 g (d) 80 g

14.12. The 400-g piston in a compressor oscillates up and down through a total distance of 80 mm. The maximum force
on the piston when it goes through 10 cycles/s is
(a) 1.0 N (c) 63 N
(b) 6.3 N (d) 126 N

14.13. A boy holding on to the end of a rope swings back and forth once every 4.0 s. The length of the rope
(a) is 2.5 m (c) is 6.2 m
(b) is 4.0 m (d) cannot be found without knowing the boy’s mass

Supplementary Problems

14.1. What change in mass is required to double the frequency of a harmonic oscillator?

14.2. The total energy of a harmonic oscillator is doubled. What effect does this have (a) on the amplitude of the oscillations
and (b) on their frequency?

14.3. A 500-g object is dropped on a vertical spring from a height of 2 m. If the maximum compression of the spring is
10 cm, find its force constant.

14.4. A toy gun uses a spring whose force constant is 100 N/m to propel an 8-g rubber pellet. If the spring is compressed
by 5 cm when the trigger is pulled, what is the pellet’s initial velocity?

14.5. A 5-lb object is suspended from a spring whose force constant is 40 lb/ft. Find (a) the amount by which the spring
is stretched, (b) the elastic potential energy of the stretched spring, and (c) the period of oscillation of the system.

14.6. A 30-g mass is suspended from a spring whose force constant is 20 N/m. Find (a) the amount by which the spring
is stretched, (b) the elastic potential energy of the stretched spring, and (c) the period of oscillation of the system.