Free and Forced Vibrations

This structure investigates the free and forced vibrations of a rigid beam with a spring, and a simply supported beam.

Learning Outcomes

  • Free and forced vibrations of a rigid beam and spring
  • Free and forced vibrations of a flexible pinned-pinned (simply supported) beam
  • Frequency of oscillation and varying mass
  • Phase difference between displacement, its derivatives and measured acceleration
  • Damped free and forced oscillations and damping coefficient
  • Phase relationship between the applied force and beam position for different damping values


A bench-top unit to demonstrate free and forced vibrations of two mass-beam systems:

  1. A ‘rigid’ beam with a pivot at one end and a spring at the other – the spring provides elasticity.
  2. A ‘flexible’ pinned-pinned beam with a pivot at one end and a roller pivot at the other – the beam itself provides the elasticity.
Free and Forced Vibrations Image


  • Two different vibration systems in one self-contained unit: a ‘rigid’ beam with a spring and a pinned-pinned ‘flexible’ beam
  • Non-contacting displacement sensor
  • High-quality servomotor ‘exciter’ – for forced vibrations at a constant speed
  • Built-in accelerometer for comparison of derived and measured acceleration waveforms

Essential Ancillaries:

  • Versatile Data Acquisition System – bench-mounted version
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