Is This the Correct Differential Equation for a Mass-Spring Oscillation Lab?

[formulajoe]

this is for a lab, but i wrote down the wrong equation. the lab was about attaching a 200 gram mass to a spring. we had to displace it so many cm, and than release it. we had to measure the period of the oscillations. but we are supposed to compare this measured period with a period obtained from the solution of the appropriate differential equation. i wrote down this for the diff eq, but I am not sure if its right

-kx -b(dx/dt)^2=m(d^2x/dt^2)

is this the correct one? and if it is, where can i find the solution to this?

 

[cookiemonster]

The equation for undamped simple harmonic motion is:

$$m\!\stackrel{..}{x} +\, \omega_0^2x = 0$$

It can be solved by attempting a solution of the form $y = A\cdot \textrm{cos}(\omega x + \phi)$

cookiemonster

 

[formulajoe]

this needs to include friction. that's the b*v^2. i can't find anything anywhere that has a differential equation with friction.

 

[cookiemonster]

Just add a term:

$$m\!\stackrel{..}{x} +\, \omega_0^2x + b\!\stackrel{.}{x}^2 = 0$$

cookiemonster