Question
A particle of mass m is placed in a potential V(x) =
ax² + bx⁴. For small oscillations around equilibrium, its time period is:Solution
Potential energy: V(x) = a·x² + b·x⁴ Mass = m We are to find time period for small oscillations around equilibrium. Find equilibrium point Equilibrium occurs where dV/dx = 0 dV/dx = 2a·x + 4b·x³ = x(2a + 4b·x²) ⇒ x = 0 is the equilibrium point 
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