Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN: 9781305627734
Author: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher: Cengage Learning
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Transcribed Image Text:The force of a spring obeys Hooke's law: F
=
-kx for some positive
constant > 0, where x = x(t) measures the displacement from its rest
position of a particle of mass m > 0 attached to the spring.
i. Use Newton's Second Law to show that the equation of motion of
the particle is
+w²x=0.
Determine w in terms of k and m. Find the solution to this equation
if the particle is released at time t 0 from position x = 4 with
=
velocity 2w.
ii. Show that
=
1
w2
E =
+
2
is a conserved quantity of the motion. What is the value of E for the
above solution. What is the meaning of the two terms on the right
hand side?
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