Pendulum Point of Suspension & Acceleration: Time Period Explanation

[nishant]

if a pendulum's point of suspension is moving upwards with acceleration {a},then the time period of the simple pendulum will increase or decrease?{many people are using pseudo force to calculate this question,but that is to be used only when we are also moving with the point of suspension,but no where in the actual question is it written theat way?"

 

[Chi Meson]

The point of view is not important here. The fact that the pendulum is accelerating is key. General relativity says that we can not tell the difference between the effects of being in a gravitational field and the effects of actual acceleration. If the pendulum accelerates upward, then the pendulum will behave exactly as it would in a gravitational field of "g+a."

Of course this will be ignoring the effects of air resistance.

 

[ramollari]

OK, if you want to prove it the hard way you can apply Newton's laws with the observer in an inertial frame of reference. Vertically, Ty - mg = ma. Use this to determine Tx in terms of displacement and you'll arrive at the same result

$$T = 2\pi \sqrt{\frac{L}{g + a}}$$

On the other hand virtual gravity (grav. acceleration = g+a) is a convenient abstraction that you could use.