5.5. Simple Harmonic Motion http://www.ck12.org
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Example Problem: When a 500. kg crate of cargo is placed in the bed of a pickup truck, the truck’s springs
compress 4.00 cm. Assume the springs act as a single spring.
(a) What is the spring constant for the truck springs?
(b) How far with the springs compress if 800. kg of cargo is placed in the truck bed?
Solution:
(a)k=Fx=(^500 .kg)(^9.^80 m/s
(^2) )
0. 0400 m =^1.^23 ×^10
(^5) N/m
(b)x=Fk=(^800 .kg)(^9.^80 m/s
(^2) )
- 23 × 105 N/m =^0 .064 m=^6 .4 cm
Summary
- Simple harmonic motion occurs in many situations, including an object of the end of a spring, a tuning fork,
a pendulum, and strings on a guitar or piano. - A mass oscillating on a horizontal spring is often used to analyze SHM.
- The restoring force for a mass oscillating on a horizontal spring is related to the displacement of the mass
from its equilibrium position,F=−kx. - SHM is related to uniform circular motion when the uniform circular motion is viewed in one dimension.
Practice
Questions
Use this resource to answer the questions that follow.
https://www.youtube.com/watch?v=BRbCW2MsL94
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/112419- What is the graph produced by a swinging pendulum’s motion graphed over time?
- How does the Exploratorium demonstrate the relationship between simple harmonic motion and circular
motion? Is it convincing? - Why don’t the pendulums all swing at the same rate?
The following website has a set of questions and answers about simple harmonic motion.
http://www.education.com/study-help/article/simple-harmonic-motion_answer/