Worksheet: Damped Oscillations

In this worksheet, we will practice calculating the energy lost due to dampening by resistive forces in systems exhibiting simple harmonic motion.

Q1:

The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?

Q2:

If a car has a suspension system with a force constant of 5.00×10 N/m, how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?

Q3:

A car with a mass of 1,530 kg bounces vertically with an initial velocity of 0.940 m/s, returning to its original vertical position after bouncing. How much energy must the car’s shock absorbers dissipate in order to dampen the bounce? Assume that the drag is negligible.

Q4:

What quantity is the damping force in damped and forced vibrations proportional to?

  • Avelocity of the vibrating object
  • Bmomentum of the vibrating object
  • Cmass of the vibrating object
  • Dweight of the vibrating object
  • Edisplacement of the vibrating object

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