Waves Practice Problem Set Worksheet Page 5
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ECHANICS
RACTICE
ROBLEM
ETS
2. How long would a pendulum have to be if it has a frequency of 2 Hz?
Answer: 0.062 m
3. A simple pendulum with a bob mass of 0.5 kg and a string length of 1.0 m and is
taken to the moon, which has an acceleration due to gravity that is 1/6 that of the
acceleration due to gravity on Earth. If you want to maintain the same period on
Moon that you have on Earth, what adjustment will you have to make to the…
a. Mass of the pendulum bob?
Answer: None
b. Length of the string?
Answer: Shorten to 0.166 m
7.1.3 SHM Review Problems
1. (G1) When a 65-kg person climbs into a 1000-kg car, the car’s springs compress
vertically by 2.8 cm. What will be the frequency of vibration when the car hits a
bump? Ignore damping.
Answer: 0.74 Hz
2. (G7) A balsa wood block of mass 50 g floats on a lake, bobbing up and down at a
frequency of 2.5 Hz.
a. What is the value of the effective spring constant of the water?
Answer: 12 N/m
b. A partially filled water bottle of mass 0.25 kg and almost the same size and
shape of the balsa block is tossed into the water. At what frequency would you
expect the bottle to bob up and down? Assume SHM.
Answer: 1.1 Hz
3. (G9) A 0.50-kg mass at the end of a spring vibrates 3.0 times per second with an
amplitude of 0.15 m. Determine:
a. The velocity when it passes the equilibrium point. Answer: 2.8 m/s
b. The velocity when it is 0.10 m from equilibrium. Answer: 2.1 m/s
c. The total energy of the system.
Answer: 2.0 J
d. The equation describing the motion of the mass. Assume φ = 0.
Answer: (0.15 m) cos [2 π (3.0 Hz)t]
4. (G13) It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to
“load” a 0.150-kg ball. With what speed will the ball leave the gun?
Answer: 10.3 m/s
5. (G15) A mass sitting on a horizontal, frictionless surface is attached to one end of a
spring; the other end of the spring is fixed to a wall. 3.0 J of work is required to
compress the spring by 0.12 m. If the mass is released from rest with the spring
2
compressed, it experiences a maximum acceleration of 15 m/s
. Find the value of:
2
a. The spring constant.
Answer: 4.2 x 10
N/m
b. The mass.
Answer: 3.3 kg
6. (G17) A 0.50-kg mass vibrates according to the equation x=0.45cos(8.40t), where x is
in meters and t is in seconds. Determine:
a. The amplitude.
Answer: 0.45 m
Gamzon & Gregorian-Michaelsen
6/7/16
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