PHYS 1112 SHM and Waves Self Assessment Practice Problems

Self Assessment Practice Problems for Simple Harmonic Motion & Waves

1
A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?
Answer: 2.37 N/m

2
A diver on a diving board is undergoing SHM. Her mass is 55.0 kg and the period of her motion is 0.800 s. The next diver is a male whose period of simple harmonic oscillation is 1.05 s. What is his mass if the mass of the board is negligible?
Answer: 94.7 kg

3
A novelty clock has a 0.0100-kg-mass object bouncing on a spring that has a force constant of 1.25 N/m.
(a) What is the maximum velocity of the object if the object bounces 3.00 cm above and below its equilibrium position?
(b) How many joules of kinetic energy does the object have at its maximum velocity?
Answer: (a) 0.335 m/s (b) 5.61 x 10-4 J

4
A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?
Answer: 0.389 kg

5
The position of a 0.30-kg object attached to a spring is described by x = (0.25 m) cos (0.4π t). Find
(a) the amplitude of the motion
(b) the spring constant
(c) the position of the object at t = 0.30 s
(d) the speed of the object at t = 0.30 s
Answer: (a) 0.25 m. (b) 0.47 N/m. (c) 0.23 m. (d) 0.12 m/s

6
A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of 8.50 cm. If the cork is 10.0 m from the shore, how long does it take a ripple passing the cork to reach the shore?
Answer: 58.8 s

7
A thin, 80.0-cm wire has a mass of 16.3 g. One end is tied to a nail, and the other end is attached to a screw that can be adjusted to vary the tension in the wire.
(a) To what tension must you adjust the screw so that a transverse wave of wavelength 3.35 cm makes 630 vibrations per second?
(b) How fast would this wave travel?
Answer: (a) 9.1 N (b) 21.1 m/s

8
An astronaut on the moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00 grams is 1.60 m long and has a 3.00-kg object suspended from it. A pulse requires 36.1 ms to traverse the length of wire. Calculate gmoon from these data. (You may neglect the mass of the wire when calculating the tension in it.)
Answer: 1.6 m/s2

9
A series of pulses of amplitude 0.15 m is sent down a string that is attached to a post at one end. The pulses are reflected at the post and travel back along the string without loss of amplitude. What is the amplitude at a point on the string where the two pulses are crossing if
(a) the string is rigidly attached to the post?
(b) the end at which reflection occurs is free to slide up and down?
Answer: (a) 0 (b) 0.30 m