# Algebra HELP for physics homework

1. Oct 16, 2011

### 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
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 16, 2011

### DukeLuke

3. Oct 16, 2011

### danpab

i have no idea where to start :S

4. Oct 16, 2011

### 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.

5. Oct 16, 2011

### danpab

ok ill try that thanks :)

6. Oct 16, 2011

### 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??

7. Oct 16, 2011

### 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.

8. Oct 16, 2011

### danpab

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