Potential energy (U) of a body of unit mass moving in a one-dimension conservative force fileld is given by, U = `(x^(2)` – 4x + 3). All units are in S.I. (i) Find the equilibrium position of the body. (ii) Show that oscillations of the body about this equilibrium position is simple harmonic motion & find its timeperiod. (iii) Find the amplitude of oscillations if speed of the body at equilibrium position is `2 sqrt(6)` m/s.

Explanation

(i) `x_(0) =2m` (ii) T = `sqrt(2)pi` sec (iii) `2sqrt(3)`