ACCELERATING MOTION OF A PARTICLE IN THE GRAVITATIONAL FIELD

Virtual mass = Mass of particle + Added mass. 

It may be noted that the equations of motion for the two directions (X and F) are coupled, with x and y appearing in each of the equations. General solutions are therefore not possible, except as will be seen later for motion in the Stokes law region. 

If allowance is made for the added mass and m is substituted for m in equation 3.78, then  

In this particular case, the equations of motion for the X and Y directions are mutually independent and therefore can be integrated separately. Furthermore, because the frictional term is now a linear function of velocity, the sign will automatically adjust to take account of whether motion is downwards or upwards. 

The equations are now integrated, ignoring the effects of added mass which can be accounted for by replacing a by a and b by b. For the 7-direction, integrating equation 3.86 with respect to t  

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