# physics

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A simple pendulum with a length of 1.50 m is suspended from the ceiling of a train. What is the period of simple harmonic motion for the pendulum if the train is moving up an incline of 15.0˚ with an acceleration of 3.00 m/s²?

• physics -

The pendulum will act as if the gravitational acceleration were the vector sum of g (down) and -a, aimed 15 degrees below horizontal. Call the resultant g'

g' = sqrt (g^2 + a^2 - 2 ag cos 105) = 10.96 m/s^2

Then use g' instead of g in the formula for the period.

P = 2 pi sqrt (L/g')

Just adding the vertical component of a to g will not get you the right answer for g'.

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