Algebra HELP for physics homework

[danpab]

I need help on this question for my postlab, thanks !
By direct substitution, show that equation (3) is a solution of the differential equation (2)


α(t)=α0 cos(√(g/l) t) (3)
(d^2 α)/(dt^2 )=-g/l α (2)

α = angle alpha in degrees
α0 = amplitude of motion
g = gravity
l = length

 

[DukeLuke]

If you want help you need to post an attempt.

 

[danpab]

i have no idea where to start :S

 

[DukeLuke]

It looks like the problem wants you to show that the solution given a(t) actually satisfies the differential equation. To show this you can take the function a(t) and put it into the differential equation, do the derivatives, and show that after taking the derivatives one side of the equation equals the other.

 

[danpab]

ok ill try that thanks :)

 

[danpab]

attempt:
α(t)=α0 cos(√(g/l) t) (3)
0=-g/l *α0 *cos(√(g/l) t) *dt^2
is this right? how do is solve for the right part??

 

[DukeLuke]

No, it's hard to tell what you're doing. This isn't a algebra problem it's a matter of evaluating derivatives and showing that these satisfy the equation. You need to take the 2nd derivative of a(t) with respect to t ($\frac{d^2a(t)}{dt^2}$) and show that this is equal to the right hand side ($\frac{-g}{l}a(t)$). You're not solving for anything, rather just showing that this a(t) satisfies the differential equation. Remember that a is not a variable it is a function.

 

[danpab]

ok, completely understood now, its been a while since I've taken calculus, u just completely jolted my memory, problem solved :) THANKS