Question

An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object?

Answer 1

Period of oscillation of a pendulum is inversely proportional to the square root of gravitational field density.

Answer 2

`T=2 \pi \sqrt{(L)/(g) }`

Explanation:

The period of oscilations in a pendulum is defined as

`T=2 \pi \sqrt{(L)/(g) }`

Where
`L` is the length of the string and
`g` is gravity.

Notice that the pendulum is oscillating due to gravity in the first place. Then, that acceleration of gravity is affected by the acceleartion of the elevator, which is
`2g`. We know that acceleration is a vector, which means the net acceleration would be
`-g` of gravity and
`2g` of the elevator, which gives us
`g`.

Having said that, the perior of oscaillations would be the same

`T=2 \pi \sqrt{(L)/(g) }`

Because, the net acceleartion is also the same but in different direction.