If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1x104 J of energy each second, how long does it take for the bridge’s oscillations to go from 0.1 m to 0.5 m amplitude?

Ahot-air balloon takes off from the ground traveling vertically with a constant upward acceleration of magnitude g/4. after time interval δt, a crew member releases a ballast sandbag from the basket attached to the balloon. how many seconds does it take the sandbag to reach the ground? (express your answer in terms of δt)

Atemperature inversion can cause a warm air mass to move over a colder air mass. this traps the colder air mass and prevents surface air from rising. this may result in which of these? a) smog b) acid rain c) freezing rain d) a thunderstorm

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.