Procedure

2. Click the Apply button

3. Calculate the unknown mass and the angle from the couple polygon and check the values  to balance the couple polygon.

4. Calculate the unknown mass and the angle from the force polygon and check the values  to balance the force polygon.

5. After submitting the correct values the system will be balanced and the vibrations will stop.

PROCEDURE FOR SOLVING BY GRAPHICAL METHOD

The magnitude and the position of the balancing mass can be found graphically by following the procedure below:

Using a suitable scale for radius of rotation of each mass, draw the space diagram showing the positions of all the given masses as shown in below figure. Here r1, r2 and r3 are the radii of rotation of mass 1, mass 2 and mass 3 respectively.

Procedure for drawing force polygon:

1. Since the centrifugal force of each mass is proportional to the product of the mass and its radius of rotation, calculate the centrifugal force.

2.  Draw the vector diagram using a suitable scale with the values obtained in step one. Measure the closing side of the polygon which represents the resultant centrifugal force.

  Force polygon (for representation)

3. The balancing force is equal to the resultant force but in the opposite in direction.

4.   Since the product of the balancing mass and its radius of rotation is equal to the closing scale of the polygon, the magnitude of balancing mass can be calculated by measuring the closing scale of the polygon and multiplying it by the scale used.

5. Transfer this closing side to the space diagram 

6.  Measure the angle of inclination of the balancing mass from the horizontal mass in the space diagram to obtain the angle of inclination of the balancing mass for force polygon.

Procedure for drawing couple polygon:

1. Calculate the product of the mass, the radius of rotation and distance from reference frame for each mass.

2.  Using a suitable scale draw the force polygon

3.  The closing side of the polygon represents the balancing couple and by measuring it and multiplying by the scale used the magnitude can be obtained.

Couple polygon (for representation)

4. Transfer this closing side to the space diagram

      5. Measure the angle of inclination of the balancing mass from the horizontal mass in the space diagram to obtain the angle of inclination of the balancing mass for couple polygon 

Final space diagram after transferring forces

6. Here mx is the balancing mass for centrifugal force and my is the balancing force for couple and i is the distance of mass from reference frame