16.8 Forced Oscillations and Resonance

A famous magic trick involves a performer singing a note toward a crystal glass until the glass shatters. Explain why the trick works in terms of resonance and natural frequency.

How much energy must the shock absorbers of a 1200-kg car dissipate in order to damp a bounce that initially has a velocity of 0.800 m/s at the equilibrium position? Assume the car returns to its original vertical position.

(a) How much will a spring that has a force constant of 40.0 N/m be stretched by an object with a mass of 0.500 kg when hung motionless from the spring? (b) Calculate the decrease in gravitational potential energy of the 0.500-kg object when it descends this distance. (c) Part of this gravitational energy goes into the spring. Calculate the energy stored in the spring by this stretch, and compare…

Engineering Application: A suspension bridge oscillates with an effective force constant of $1 . \text{00} \times \text{10}^{8} \text{N}/\text{m}$. (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 $1 . \text{00} \times \text{10}^{4} \text{J}$ 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?