A block of mass m is attached to an ideal horizontal spring of force constant k inside a vehicle accelerating uniformly with acceleration a along the spring. Relative to the vehicle, what happens to the equilibrium position and the small-oscillation time period?
Options

Question

A block of mass m is attached to an ideal horizontal spring of force constant k inside a vehicle accelerating uniformly with acceleration a along the spring. Relative to the vehicle, what happens to the equilibrium position and the small-oscillation time period?

Options

G1 Physics · Accepted Answer

In the vehicle frame, a constant pseudo-force ma acts opposite the vehicle acceleration. This changes the equilibrium condition to kx₀ = ma, so x₀ = ma/k. Let y be displacement from the new equilibrium. Then the constant pseudo-force cancels with the static spring force and mÿ = −ky. Therefore, ω = √(k/m), and T = 2π√(m/k). Correct option: B.