# A body is affekted by a non-linear spring with a force that is given by the relation: Fₓ=-cx³ with c being a positive constant.?

a) What does it mean that the constant is positive?

b) Determine the corresponding potential

c) The body that affects the spring has mass m. When it is at rest at position x=0 it gets an impact so thats its velocity momentarily is v₀. Qualitatively describe the body's movement after the impact. In particular the turning points.

Thanks!

### 1 Answer

- NCSLv 72 weeks agoBest answer
(a) simply that the force is in a direction opposite the displacement of the spring, just like any other spring.

(b) Do you mean "the corresponding potential energy as a function of x?" If so, then

E = ∫ |Fx| dx = c ∫ x³ dx = (c/4)x⁴

(c) the turning points are "sharp" or "sudden" because the energy stored in the spring is based on such a large order of x. They are also not very far apart (based on what one might expect from a Hookean spring).

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