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Chapter 4: Q17Q (page 165)
Describe two examples of oscillating systems that are not harmonic oscillators.
Examples of oscillating systems which is not harmonic are the bouncing ball, Earth in its orbit, and a swing motion.
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You hang a 10kg mass from a copper wire, and the wire stretches by 8mm. (a) If you suspend the same mass from two copper wires, identical to the original wire, what happens? (b) If you suspend the same mass from a copper wire with half the cross-sectional area but the same length as the original wire, what happens? (c) If you suspend the same mass from a copper wire with the same cross-sectional area but twice the length of the original wire, what happens?
You hang a mass Mfrom a spring, which stretches an amount . Then you cut the spring in half, and hang a mass Mfrom one half. How much does the half-spring stretch? (a) , (b) ,(c).
A certain metal with atomic mass 2 × 10-25 kg has an interatomic bond with length 2.1 × 10-10 m and stiffness 40 N/m. What is the speed of sound in a rod made of this metal?
A bouncing ball is an example of an anharmonic oscillator. If you Quadruple the maximum height, what happens to the period? (Assume that the ball keeps returning to the same height.)
It was found that a mass hanging from a particular spring had an oscillation period of . (a) When two masses are hung from this spring, what would you predict for the period in seconds? Explain briefly.
Figure 4.58
(b) When one mass is supported by two of these vertical, parallel springs (Figure 4.58), what would you predict for the period in seconds? Explain briefly. (c) Suppose that you cut one spring into two equal lengths, and you hang one mass from this half spring. What would you predict for the period in seconds? Explain briefly. (d) Suppose that you take a single (full-length) spring and a single mass to the Moon and watch the system oscillate vertically there. Will the period you observe on the Moon be longer, shorter, or the same as the period you measured on Earth? (The gravitational field strength on the Moon is about one-sixth that on the Earth.) Explain briefly.
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