Classical Mechanics; Lagrangian for a particle on a spring in the absence of gravity custom essay

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1 spring under gravity
In the lectures we derived the Lagrangian for a particle on a spring in the absence of gravity.
Now consider the particle of mass m on a spring of strength k, suspended vertically (that is,
subject to gravity). Choose an appropriate coordinate for this 1 degree of freedom system and
find the Lagrangian. Derive the equations of motion and find the equilibrium point. Using a
new coordinate u with u = 0 at the equilibrium point, find the general solution to the differential
equation. What is the period of motion?

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