If you do the pendulum experiment on a planet with a larger gravity than Earths gravity what would the graph look like?

Question

I know a graph for the length of the pendulum vs the period squared on Earth would be a positive slope .

I also know that doing this on another planet with a higher gravity than Earth , the graph will have a steeper slope. What I don't understand is : Why is it steeper? What is happening? How it changes the formula?

I don't really understand this so a detailed reposes would be very appreciated! Thank you

Answer 1

The relevant formula is

T = 2π√(L/g)

where

L is the length of the pendulum,

g is gravitational acceleration,

T is the period of the pendulum.

That is also the formula you should use for your other question about planet X.

Equivalently the formula can be written

T² = 4π²L/g

And that is apparently the formula you are referring to when saying

that T² depends linearly on L.

The graph of T² vs L will be a straight line with positive slope on any planet.

The slope is 4π²/g.

The reason is that the dependence of T² on L can be written as

T² = (4π²/g)L

On another planet with higher gravity the slope will be less steep.

In other words, it is the opposite to your expectation; perhaps that is the confusion.

If you go to another planet with gravity 4 times stronger,

your pendulum's period will be cut in half.

Or equivalently, the pendulum will oscillate twice as fast.