UniversityPhysicsVolume1-Ch15 Florida State College at Jacksonville PHY 2048C

Unit 2: Waves and Acoustics
Chapter 15: Oscillations
University Physics Volume I
Unit 2: Waves and Acoustics
Chapter 15: Oscillations
Conceptual Questions
1. What conditions must be met to produce SHM?
Solution
The restoring force must be proportional to the displacement and act opposite to the direction of
motion with no drag forces or friction. The frequency of oscillation does not depend on the
amplitude.
2. (a) If frequency is not constant for some oscillation, can the oscillation be SHM? (b) Can you
think of any examples of harmonic motion where the frequency may depend on the amplitude?
Solution
(a) If the frequency is not constant, some change in force or additional force must have changed
the frequency, which suggests that the system is not oscillating in simple harmonic motion.
(b) No, the frequency of a system in simple harmonic motion depends on the force constant and
the mass.
3. Give an example of a simple harmonic oscillator, specifically noting how its frequency is
independent of amplitude.
Solution
Examples: Mass attached to a spring on a frictionless table, a mass hanging from a string, a
simple pendulum with a small amplitude of motion. All of these examples have frequencies of
oscillation that are independent of amplitude.
4. Explain why you expect an object made of a stiff material to vibrate at a higher frequency than
a similar object made of a more pliable material.
Solution
A stiff material would have a stronger force constant, and a stronger restoring force for a given
displacement. Since the frequency of oscillations is equal to
1
2
k
f
 m

the frequency would be
higher.
5. As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing
up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain
your answer.
Solution
Since the frequency is proportional to the square root of the force constant and inversely
proportional to the square root of the mass, it is likely that the truck is heavily loaded, since the
force constant would be the same whether the truck is empty or heavily loaded.
6. Some people modify cars to be much closer to the ground than when manufactured. Should
they install stiffer springs? Explain your answer.
Solution
A stiffer spring will produce a smaller amplitude of osci