JEE Main · PhysicsHard

$A particle moves in a potential $V(x) = kx^4$. For small oscillations about the equilibrium position, what is the relationship between the period of oscillation $T$ and the amplitude $A$?$

Show correct answer & step-by-step solution

Correct answer: C — $T \propto A^{-1/2}$

Solution

For a potential

V (x) = c x^{n}

, the period of oscillation scales as

T \propto A^{1 - n /2}

. Substituting

n = 4

gives

T \propto A^{1 - 2} = A^{- 1}