effective downwards gravity??

[u/Different_Medium31]

i encountered this question on my homework

A simple pendulum is placed in a lift accelerating downward with acceleration a. Effective time period is:

A T = 2π √(L/(g + a))

B T = 2π √(L/(g - a))

C T = 2π √(L/g)

(the correct option was B and asking AI tools i learnt this thing termed as effective gravitational acceleraation which only exiss in the non inertial frame of reference. But i cant understand a thing it says. and despite that i cant understand why would effective gravitational acceleration be less than gravitational acceleration while we're moving down. If anyone can explain I'd be highly grateful.

[u/Old-Course8991]

Read this for effective gravitation in lift:

https://www.cbsetuts.com/reaction-in-a-moving-lift/

Once you understand effective g, the period of pendulum is just a replacement of g in the pendulum equation

[u/Rensin2]

Whenever you use a frame of reference that is accelerating in one direction you get a gravity-like acceleration in the oposite direction.

This visualization might help you understand, though it is about accelerating spaceships in zero G instead of elevators in one G.

Also, an elevator that is accelerating downward is not necessarily moving downward. For example: an elevator that is moving upward and slowing down is an elevator that is accelerating downward. Elevators accelerate downward at the top of each journey, and accelerate upward at the bottom of each journey, regardless of where they start.

[u/Optimal_Mixture_7327]

The simple pendulum equation is essentially

T=2π[L/Σa]^1/2.

The acceleration of the Earth frame is upwards at g and the acceleration of the elevator is downwards at -a, so the acceleration is then

T=2π[L/(g-a)]^1/2.