Waves Practice Problem Set Worksheet Page 4
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47M
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P
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1
ECHANICS
RACTICE
ROBLEM
ETS
Unit 7 SHM, W
S
AVES AND
OUND
7.1
S
H
M
IMPLE
ARMONIC
OTION
7.1.1 Mass-Spring Systems
1. An ultrasonic transducer used for medical diagnosis oscillates with a frequency of 6.7
6
x 10
Hz. How much time does each oscillation take and what is the angular
-7
frequency?
Answer: T=1.5 x 10
s;
7
ω =4.21 x 10
rad/s
2. A body of unknown mass is attached to an ideal spring that is mounted horizontally
with its left end held stationary. The spring constant of the spring is 120 N/m and it
vibrates with a frequency of 6.00 Hz. Assuming that there is no friction, find:
a. The Period
Answer: 0.17 sec
b. The Angular Frequency
Answer: 37.7 rad/s
c. The Mass of the body
Answer: 0.084 kg
3. A spring stretches 0.200 m when a 0.600 kg mass is hung from it. The spring is then
stretched 0.150 m from this equilibrium point and released. Find:
a. The spring constant (k)
Answer: 29.4 N/m
b. The amplitude
Answer: 0.150 m
c. The total energy of the system.
Answer: 0.33 J
d. Maximum velocity (v
)
Answer: 1.05 m/s
o
e. The velocity when the mass is 0.050 m from equilibrium. Answer: .99 m/s
f. The equation for the position of the mass x (t) Answer: x (t) = 0.150cos(7t)
4. A proud deep-sea fisherman hangs a 65.0 kg fish from an ideal spring with a
negligible mass. The fish stretches the spring 0.120m. What is the period of
oscillation of the fish if it is pulled down and released? Answer: 0.70 sec
5. A 0.150 kg toy is undergoing simple harmonic motion on the end of a horizontal
spring with a spring constant of 300 N/m. When the object is 0.12m from
equilibrium, it has a speed of 0.300 m/s. Find:
a. The Total energy of the system
Answer: 2.17 J
b. The Velocity of the object at equilibrium
Answer: 5.4 m/s
c. The Amplitude of the motion.
Answer: 0.120 m
7.1.2 Simple Pendulum
1. What is the period of a pendulum at sea level with a length of 1.5 m?
Answer: 2.45 sec
a. What would the period of this pendulum be if the length were shortened to a
¼ of the original length?
Answer: 1.23 sec
Gamzon & Gregorian-Michaelsen
6/7/16
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