# harmonic motion differential eq

• Mar 30th 2013, 10:06 AM
CoffeeBird
harmonic motion differential eq
A body of mass 'm' is hung on the end of a vertical spring of spring constant 'k'; the body is pulled down and released. in the resulting harmonic motion, the displacement 'y' of a body is given by the dif eq

m(d^2y)/(dt^2) + ky=0

show that the function:

y= cos(sqrt(k/m))* t

is a solution to the dif eq satisfying the boundary conditions:

y=1 when t=0 and y'=0 when t=0

i see how the differential equation comes from that info, but i'm getting lost in the algebra of trying to simplify its derivatives...
• Mar 30th 2013, 04:16 PM
Prove It
Re: harmonic motion differential eq
If all you're doing is showing that a function satisfies the DE, differentiate it to get the derivatives and substitute into the DE. See if it works...
• Mar 30th 2013, 04:39 PM
CoffeeBird
Re: harmonic motion differential eq
ok i see what i've been doing. i've been treating what's inside the square root as variables. whoops- my bad. sorry for wasting space on the forum...