A 10 kg particle moves under the influence of the potential

Question

Compute all parts of given question:

Question: A 1.0 kg particle moves under the influence of the potential V(x) = - C x² cos(3x), where C = 5 J/m².

Part A: Determine the equilibrium points for this potential function. (If you encounter a transcendental equation in the process, using MATLAB to find a numerical approximation to the solutions is recommended.)

Part B: Find the frequency of small oscillations about the equilibrium points for this particle.

Part C: Can this particle oscillate about the origin (x = 0) ? Explain briefly.

Part D: How much total energy would this particle require to be able to just reach the point x = 0.2 m?

I need help to find the frequency of small oscillations about the equilibrium points for this particle and comment on the sign of your answer.