Pendulum SHO but with extra downward acceleration of the pivot

[simphys]

Homework Statement

A pendulum is hanging fromt he ceiling of an elevator. Its period (at small angles) is T sec when the elevator is at rest. We now accelerate the elevator downward w/ 5m/s^2. What is the period now? Be quantitative. [g = 10m/s^2]

Relevant Equations

$T = 2*/pi * sqrt(l / g)$

Hey guys,
Can someone help me understand how to understand this problem intuitively please?
How I understand is that I need to look the acceleration relative to the lift as if it were f.e. on another planet with a different acceleration. this gives me a = g - 5.
But then again if I didn't look up the solution I would not have been able to solve it. So.. I don't really understand this intuitively. I actually thought (before looking at the solution) that it stays the same period T as it is dependent on the gravitational acceleration.
This kind of confuses me, and leaves me feeling that I don't really understand what what the g means in the equation.Thanks in advance.

 

[haruspex]

Think about the extreme fall case, free fall. Why would the pendulum swing at all?

 

[Lnewqban]

... I don't really understand this intuitively. I actually thought (before looking at the solution) that it stays the same period T as it is dependent on the gravitational acceleration.
This kind of confuses me, and leaves me feeling that I don't really understand what the g means in the equation.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c3

For a simple common pendulum, gravity is the only acceleration that gets combined with its mass to produce a restoring force.
Our elevator introduces another acceleration, which vector is aligned with the gravity acceleration vector.

Therefore, a summation of those vectors would result in an increased or decreased net acceleration acting on the center of mass of our pendulum.

If the elevator is accelerating the pendulum upwards, it should be "feeling" heavier, just like you do when riding one of those, and vice-verse.

In one case, both acceleration vectors point in the same direction (vectors addition applies).
In the other case, they point in opposite directions (vectors subtraction applies).