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

## Objective

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.

## Entities Validated

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

## Type of Analysis

- Dynamic

## Reference

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

## Result Comparison

Output | Analytical | MotionSolve | % Error |
---|---|---|---|

Amplitude of fluctuating force (N) | 71.8 | 71.8 | 0 % |

## Conclusion

MotionSolve results compare well with analytical results.