# Help on solving differential equations...

• Oct 18th 2008, 11:58 AM
ben218
Help on solving differential equations...
I am doing a project on projectiles in sport and have set up the following differential equations when investigating the projectile of a golf ball with air resistance:

mx'' = -kx' and my'' = -mg -ky'

with initial conditions:
x(0)=0
x'(0)=u0=ucos(alpha)
y(0)=0
y'(0)=vo=usin(alpha)

Could someone help me solve these differential equations and show me the method in which it is done. I am really not sure how to do them.

Thanks
• Oct 18th 2008, 12:40 PM
galactus
$m\frac{d^{2}t}{dt^{2}}=-kx$

has well known solutions of

$x(t)=C_{1}cos(\sqrt{\frac{k}{m}}t)+C_{2}sin(\sqrt{ \frac{k}{m}}t)$

Now, find x'(t) and use your initial conditions to find $C_{1}, \;\ C_{2}$
• Oct 18th 2008, 12:47 PM
ben218
Sorry can you explain that please. Not sure what you mean. Could you go through solving each equation step by step if possible please, i have attempted them and must have gone wrong at one of the early steps...

Thanks
• Oct 19th 2008, 04:46 PM
mr fantastic
Quote:

Originally Posted by galactus
$m\frac{d^{2}t}{dt^{2}}=-kx$

has well known solutions of

$x(t)=C_{1}cos(\sqrt{\frac{k}{m}}t)+C_{2}sin(\sqrt{ \frac{k}{m}}t)$

Now, find x'(t) and use your initial conditions to find $C_{1}, \;\ C_{2}$

Big G, you've misread the right hand side of the DE. It's x', not x.