For a particle constrained to move along the -axis

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

For a particle constrained to move along the

x

-axis, the net force is

F(x)=x^{3}-4x

(in newtons), with

x

in meters. Which list identifies all equilibrium positions and correctly classifies their stability? (a)

x=0\,\text{m}

(unstable);

x=\pm2\,\text{m}

(stable) (b)

x=\pm\sqrt{\dfrac{4}{3}}\,\text{m}

(stable);

x=0\,\text{m}

(unstable) (c)

x=0\,\text{m}

(stable);

x=\pm2\,\text{m}

(unstable) (d)

x=\pm2\,\text{m}

are stable equilibria;

x=0\,\text{m}

is neutral