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A particle of mass m moving in one dimension is subject to the potential (x) = V₁²²2e-², a>0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.

A particle of mass m moving in one dimension is subject to the potential (x) = V₁²²2e-², a>0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.

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A particle of mass m moving in one dimension is subject to the potential V(x) = Voe-, a> 0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.
Transcribed Image Text:A particle of mass m moving in one dimension is subject to the potential V(x) = Voe-, a> 0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.
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