Question

Calculate the g effective for upward lift for simple pendulum

Answer 1

Fun fact: in a reference frame undergoing uniform acceleration, the effect of the acceleration is indistinguishable from gravity**, e.g. if you’re out in deep space, and your shuttle is accelerating “upward” at 9.8 m/s², you will feel just as if the shuttle were sitting on the surface of Earth.

We have the equation for the period of a pendulum

T=2πLg−−√

Suppose the lift accelerates upward with acceleration a. This upward acceleration effectively adds to the gravitational acceleration.

T′=2πLg+a−−−√

We can examine the ratio of the periods.

T′T=11+a/g−−−−−√

So if, for example, a=g, then the period will decrease by 29%. Increasing the acceleration decreases the period.