Page 20 - C:\Users\trainee\AppData\Local\Temp\msoEAA3.tmp

Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics

Separating the variables of velocity and time in equation (2.19), we get:

dv
kv 2 = dt , the time of travel is got by integrating both sides.
g −
m

v 0 t
dv k
= 2 = dt , taking in the LHS common, we get:
g − kv m
U 0 m 0

v 0
m dv
= t - - - - (2.20)
k gm − v
2
U 0 k
To reduce equation (2.20) to a standard integral form, it is rewritten as follows:

v 0
m dv dx 1 −1 x

k 2 = t , this is a standard integral of the form: a − x = tanh
2
2
a
a
U 0 gm 2 1
2
k − v

Using the standard formula for the integral, we get:

v 0
m dv m 1 −1 v 0 −1 U 0
tanh

k 1 2 = t = k ∗ mg mg − tanh mg = t

U 0 gm 2 2
k − v k k k

Page 20 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,