- #1
frostking
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Homework Statement
A particle has potential energy
U(x) = x + sin ((2 rad/m) x)
over the range of x greater or equal to 0 meters and less than or equal to pi meters
Where are the equilibrium positions in this range and for each is it a point of stable or unstable equilibrium?
Homework Equations
derv of u(x) set = to 0 and then the second derv of u(x)
The Attempt at a Solution
I solved derv of u(x) = 1 + 2 cos(2x) then set = to 0
so 2 cos(2x) = -1 divide by 2 and cos(2x) = -1/2
2x = arch cos of (-1/2) = 2pi/3 rad
x = 1 pi/3 rad
I get this part but the answer says that x can = 2pi/3 rad as well and I do not understand why.
To determine if equilibrium is unstable or stable I took the second derv and at x = pi/3 and second derv of - 4 sin(2x) I got less than 0 so a maximum and therefore unstable equilibrium
Can someone please help me understand why I should have known to consider 2pi /3? Thanks for your efforts, Frostking