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I've tried to do this using total force on the bob = tension + mg + ma, where a is the acceleration of the plane. Resolving mg and ma into components I came out with:

g sin 22 = a cos 22

which gives me a = 3.96m/s^2.

Then using T = 2 pi (L/(g+a))^1/2

I found T = 1.42s, however the solution given in the book for this problem says T = 1.62s. Where have I gone wrong?