# Why can't a pendulum vibrate in a an orbiting satellite?

People say because the pendulum would not feel any gravity, so the time period becomes infinite. However, I think the pendulum would be in a state of free fall, it would certainly feel gravity, what can possibly hamper the oscillatory motion is absence of net tension. Is there any merit to my explanation?

$T$ $- mg$= $-mg$

Thus, $T=0$

So, would the pendulum sling itself upwards or execute any random motion?

• One more question, is there any real life example of undamped free oscillations? Would a pendulum oscillating in vacuum on earth be a legit example? Nov 23, 2014 at 11:11
• Undamped oscillations do arise in quantum systems between measurement events. Here the oscillations are such that the integral over the whole quantum state spacespace of the squared magnitude wavefunction has to equal 1, because this represents the probability that the system is in some state (it always has to be, of course). In other examples: the Earth has been in pretty much uniform circular motion about the Sun for $4.5\times 10^9$ years: that's a pretty near to undamped oscillation. Nov 23, 2014 at 11:59
• Example of the earth about the sun is periodic but not oscillatory. Nov 23, 2014 at 12:00

The "apparent" absense of gravity is explained (in classical mechanics) as being cancelled by a pseudoforce in the opposite direction, because you are inside a non inertial, accelerated, system of reference. In order for a pendulum to oscilate, it requires two forces, one is the tension (a central force), such as the tension from the rope, and gravity, which keeps push the bob downwards. Now, in absence of gravity, there is nothing to push the bob downwards. When you have a central and cosnatnt atractive force, the movement is circular. In your example the testion will be zero if the bob is at rest (you either stop it or it was not oscillating). But if you give the bob an impulse, ther cord will be tensed, regardless of the absense of gravity. In particular, if you give the bob a motion that is perpendicular to the rope, it will undergo a uniform circular motion, because the cord will have a tension (and there is no gravity to make it go back and forth).

• sounds interesting, please elaborate, I am layman. Nov 23, 2014 at 11:15
• sure, what part specifically is unclear or you want more details?
– user65081
Nov 23, 2014 at 11:16
• When you say 'the apparent absence of gravity will stop..." what does this actual boil down to? Will this make tension zero, or something else? Nov 23, 2014 at 11:18
• because the bob will try to go away, it is equivalent as if you pull the bob. When the movement is circular this is more difficult to see (less intuitive), but you can think of it this way: if the cord were not there, the bob would keep moving in a straight line away from the center (not radially, but still getting farther way), so the rope will get tense to stop this from happening.
– user65081
Nov 23, 2014 at 12:13
• The fact that it will keep moving in a circular path forever is less intuitive, and I do not know how to explain it withouth involving math.
– user65081
Nov 23, 2014 at 12:13