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In simple harmonic motion, one of the formulas of Time period of a pendulum is (T=2 pi underoot l/g)
If a lift is moving with upward acceleration, a, then a pendulum inside it will have g=9.81+a because of the total value of g, acceleration of 9.81 m/s sq. was used to cancel acceleration due to gravity so it will also be added into a.
But if a lift is moving with downward acceleration, a, why will the value of g be 9.81-a?
The force that makes the pendulum swing is centripetal, therefore any force acting or acceleration produced is directed towards the centre of circle ( in this case, it's imaginary and the pendulum is the radius).
Hence, acceleration would be in the direction against gravity and total gravity would equal to 9.81-a (downward-upward).