Question:
the period(T) of a pendulum moving in a vertical
accelerator will depend on whether the acceleration is upwards or downwards.
My question is, what happens to the period when it is experiencing a
constant horizontal acceleration? Will the pendulum not be affected
because the two main issues are length and gravity, where gravity is
always acting downwards..

Replies:
In a constant horizontal acceleration, the net effective force will be "mg"
downward added to
"ma" horizontally. Add these two vectors, and you have the force that the
pendulum "thinks it is feeling". It will be directed at an angle. The
magnitude replaces "mg". The magnitude divided by mass replaces "g" in the
period formula.

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