How Does Acceleration Affect Pendulum Frequency?

[akan]

Homework Statement

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.

Homework Equations

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

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. :)