(b) A particle of unit mass moving in one dimension obeys the equation of motion (i) Show that i2 – et is a constant of the motion. (ii) At t = 0 the particle is at x = O and at rest, i.e. x(0) = &(0) = 0. Show that %3D the particle reaches x = +0o at finite t > 0. Hint: use the result of part (i) to write the time taken to reach x = +∞ as an integral. (iii) What is a suitable Lagrangian for this system?
(b) A particle of unit mass moving in one dimension obeys the equation of motion (i) Show that i2 – et is a constant of the motion. (ii) At t = 0 the particle is at x = O and at rest, i.e. x(0) = &(0) = 0. Show that %3D the particle reaches x = +0o at finite t > 0. Hint: use the result of part (i) to write the time taken to reach x = +∞ as an integral. (iii) What is a suitable Lagrangian for this system?
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Transcribed Image Text:(b) A particle of unit mass moving in one dimension obeys the equation of motion
x =
(i) Show that i2 – e" is a constant of the motion.
(ii) At t = 0 the particle is at x = 0 and at rest, i.e. x(0) = ¿(0) = 0. Show that
the particle reaches x = +o at finite t > 0.
Hint: use the result of part (i) to write the time taken to reach x = +0 as an
integral.
(iii) What is a suitable Lagrangian for this system?
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