(i) A particle of mass m satisfies the equation of motion mä + kx = 0, (1) where x = x(t) and k is a constant. What is the usual physical inter- pretation of this differential equation? What range of values do m and k take in this case? (ii) Find (t) that solves equation (1), when the particle is released at time t = 0 from position x = 4 and velocity = 7. (iii) Show that m E = 1/2 -x² k 2 is a conserved quantity of the motion described by equation (1). What is the meaning of the two terms on the right hand side? (iv) What is the value of E for the solution you found in (ii) ?

(i) A particle of mass m satisfies the equation of motion mä + kx = 0, (1) where x = x(t) and k is a constant. What is the usual physical inter- pretation of this differential equation? What range of values do m and k take in this case? (ii) Find (t) that solves equation (1), when the particle is released at time t = 0 from position x = 4 and velocity = 7. (iii) Show that m E = 1/2 -x² k 2 is a conserved quantity of the motion described by equation (1). What is the meaning of the two terms on the right hand side? (iv) What is the value of E for the solution you found in (ii) ?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 31PQ

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