Pendulum Question

[akan]

1. The problem statement, all variables and given/known data
While waiting for your plane to take off, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute. You repeat the experiment as the plane accelerates down the runway, and now find the pendulum completes exactly 97 cycles in 1 minute.

Find the plane's acceleration.


2. Relevant equations
T = 2 pi sqrt(L/g)
T = 1 / freq.


3. The attempt at a solution
T1 = 2 pi sqrt(L/g)
(T1 / (2 pi))2 g = L

T2 = 2 pi sqrt(L/(g + a))
a = L / (T2 / (2 pi))2 - g
a = (T1 / (2 pi))2 g / (T2 / (2 pi))2 - g

I get that a = 1.58, but that's wrong. The right answer is 5.8. What did I do incorrectly?

[Redbelly98]

Think of g and a as vectors. What directions do they point in? What's the correct way to add vectors that point in those directions?

[akan]

sqrt(g^2 + a^2)?

[Redbelly98]

Yes.

[akan]

Wow. That does give me the right answer. Thanks a lot. :)