# 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,

SOURCE- INPHO 2011