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?
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?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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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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