- #1
roflol12
- 3
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Hi guys i am a bit confused about this problem,
a particle of mass, m, moves in potential a potential u(x)=k(x4 - 7 x2 -4x)
I need to find the frequency of small oscillations about the equilibrium point.
I have worked out that x=2 corresponds to the equilibrium point as
- dU/dx = F = -k(4x3 - 14x -4)=0 at x=2
I tried to solve using the Lagrangian with
L=1/2 m v2 -k(x4 - 7 x2 -4x)
using Euler–Lagrange equation d/dt(dL/dv)=dL/dx
to get: ma= -k(4x3 - 14x -4)
I thought about dropping the x^3 term as it would be very small with small oscillations but was confused what that left me with.
Any help appreciated!
a particle of mass, m, moves in potential a potential u(x)=k(x4 - 7 x2 -4x)
I need to find the frequency of small oscillations about the equilibrium point.
I have worked out that x=2 corresponds to the equilibrium point as
- dU/dx = F = -k(4x3 - 14x -4)=0 at x=2
I tried to solve using the Lagrangian with
L=1/2 m v2 -k(x4 - 7 x2 -4x)
using Euler–Lagrange equation d/dt(dL/dv)=dL/dx
to get: ma= -k(4x3 - 14x -4)
I thought about dropping the x^3 term as it would be very small with small oscillations but was confused what that left me with.
Any help appreciated!