Forced Oscillations and Resonance (Problem 46)

Engineering Application: A suspension bridge oscillates with an effective force constant of $1.00\times {10}^8\text{N/m}$. (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (b) If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart $1.00\times {10}^4\text{J}$ of energy each second, how long does it take for the bridge’s oscillations to go from 0.100 m to 0.500 m amplitude? Select the answer to part (a).