1. The problem statement, all variables and given/known data A particle of mass m is constrained to move along the x-axis. The potential energy is given by, V (x) = a + bx + cx2, where a, b, c are positive constants. If the particle is disturbed slightly from its equilibrium position, then it follows that (a) it performs simple harmonic motion with period 2pi*Sqrt(m/2c) (b) it performs simple harmonic motion with period 2pi*Sqrt(ma/2b^2). (c) it moves with constant velocity (d) it moves with constant acceleration 2. Relevant equations Force=-Gradient of V(x) F=-(b+2cx) a=-(b+2cx)/m T=2pi*Sqrt(Displacement/Acceleration) 3. The attempt at a solution I cannot proceed further. For an object to perform SHM 'a' should be proportional to -x. But how do I find this proportionality over the sum.