A particle of mass m is released from rest and follows a parabolic potential-energy path V(x) = c x² as shown. Assuming that the displacement from the origin is small, which graph correctly depicts x(t)?
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Question

A particle of mass m is released from rest and follows a parabolic potential-energy path V(x) = c x² as shown. Assuming that the displacement from the origin is small, which graph correctly depicts x(t)?

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G1 Physics · Accepted Answer

Step 1: For a parabolic potential V(x) = cx² with c > 0, force F = −dV/dx = −2cx. Step 2: Equation of motion: m d²x/dt² = −2cx, so this is SHM with ω = √(2c/m). Step 3: The particle is released from rest at an extreme position, hence initial velocity is zero. Step 4: Its position follows x = A cos(ωt), a smooth sinusoidal curve starting from maximum displacement. Step 5: That is graph (D). Final answer: (D) Image 4.