You decide to describe the harmonic motion of a swing. You tell your little sist
ID: 1990502 • Letter: Y
Question
You decide to describe the harmonic motion of a swing. You tell your little sister to get on the swing and you push her like the nice sibling you are. You quit pushing and note the following:It seems to take the swing 5 s to complete one cycle
The swing reaches 35° at the high point and 35° to the low point
The swing starts to slow down and eventually stop
18. The period of the swing:
a. 2.5 s
b. 10s
c. 0.25 s
d. 5 s
19. The amplitude of the swing:
a. 35 degrees
b. 30 degrees
c. 15 degrees
d. None of the above
20. The frequency of the swing:
a. 1.5 Hz
b. 0.20 Hz
c. 1.0 Hz
d. 0.25 Hz
21. Term explaining why the swing stops:
a. pushing
b. force
c. harmonic motion
d. damping
22. How does the swing stop if you or your sister does not physically stop it?
a. Friction from the bugs in the air
b. Friction from your sister sitting in the swing
c. It just stops
d. Friction from the air
23. If the sister’s frequency on the swing is 1.5 hertz, and she is launched from 35°, where would you expect to see the swing after 1 second?
a. 15° in the opposite direction
b. It will have traveled to -35 degrees then back to the launch point
c. It will have traveled to 0 only
d. It will have traveled to -35 degrees, then back to the launch point, then back to -35 degrees
Explanation / Answer
18. (d) 5 s
The period of harmonic motion is defined as the time needed for one cycle to be completed. This time was given as 5 seconds.
19. (a) 35 degrees
The amplitude of angular displacement is the furthest angle the swing can travel. In this case, because it reaches 35 degrees at its high and low points, the amplitude is 35 degrees.
20. (b) 0.20 Hz
The frequency is defined as the number of cycles that are completed in one second. Because we already know the period, we can easily solve for frequency:
f = 1/(5 s/cycle) = (1/5) cycles/s = 0.20 Hz
21. (d) damping
Realistic harmonic oscillators, like spring-mass systems and pendulums (as in this case), forces like friction act on the oscillator and reduce its amplitude over time. This is the reason why swings eventually slow to a stop; the next question asks how such a damping effect occurs.
22. (d) friction from the air
Air resistance is constantly acting on the swing, as the body and seat collide with many air particles as it swings through the air. This is why the damping effect occurs; the restoring force provided by tension in the string is counteracted by the force of air resistance each time, thus decreasing the total mechanical energy, and thus the amplitude of angular displacement, of the system.
23. (d) It will have traveled to -35 degrees, then back to the launch point, then back to -35 degrees
Let's think about what our given information means. If the frequency is 1.5 Hz, then by definition she travels 1.5 cycles in one second. So after that 1 second passed, she already moved through 1.5 cycles. Because the amplitude is given as 35 degrees again, she starts from 35 degrees, cycles to the -35 degree side (in 0.5 seconds; half the cycle), returns back to the 35 degree starting point (the full cycle), and then cycles back to the -35 degree end (the final 0.5 seconds after 1 s, making a 1.5 trip).
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