Trapped in the potential well

Classical Mechanics Level 4

A particle can execute one dimensional motion in a potential given by

\(U(x)\quad =\quad { x }^{ 2 }-\frac { x }{ 2 } -\frac { { x }^{ 3 } }{ 3 } \)

Assume that the mechanical energy of the particle was 0 at t=0 Further assume, that the particle is subject to No Other influence Then what is the region of space (in terms of range of 'x') where the particle performs oscillatory motion if released, let it be \((a,b)\)

Now , what is the value of x beyond (to the right of ) which, if the particle is released, it will depart to infinity, Let it be c

Then find, a+b+c

HINT- plotting a graph will allow you to answer in less than 5 seconds,



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