Problem 9: Dynamic Analysis of Damped, Forced Vibration in a Mechanism


A 91 Kg machine element supported by four springs, each of constant k = 175 N/m, is subjected to a periodic force of frequency 0.8 Hz and amplitude 89 N. Determine the amplitude of fluctuating force transmitted to the foundation if a dashpot with a coefficient of damping c = 365 N . s/m is connected to the machine element and to the ground.

Figure 1.

Entities Validated

  • Rigid body
  • Force_Spring damper – translational
  • Translational joint
  • Force vector one body

Type of Analysis

  • Dynamic


Vector Mechanics for Engineers: Statics | Dynamics, Twelfth Edition by Beer, Johnston, Mazurek, Cornwell, Self: 1422

Model Files

damped_forced_vibration.mdl - MotionView Model

damped_forced_vibration.xml - MotionSolve Deck

Graphical Results

Figure 2.

Result Comparison

Output Analytical MotionSolve % Error
Amplitude of fluctuating force (N) 71.8 71.8 0 %


MotionSolve results compare well with analytical results.