An object of mass m=80 kg moves in one dimension subject to the potential energy
U(x)=(λ/4)(x^2-a^2)^2+(b/2)x^2
Here we use λ=3kg/(m^2s^2), a=7m, and b=77kg/s^2.
(b) Find a stable equilibrium point x0 such that x0 is positive. (in meters)
x0=
(c) Do a Taylor expansion of the force F(x) for x close to the equilibrium point, x≃x0, that is F(x)=F0−k(x−x0)+… What are the values for F0 (in Newton) and k (in kg/s2)?
F0=
k=
(d) What is the period T of small oscillations (in seconds) of this mass around the equilibrium point x0? (Note that the parameter k found in the previous question acts like a spring constant that wants to pull small deviations back to the equilibrium point)
T=