The period of a pendulum is given by $$ T = 2\pi \sqrt{\frac{L}{g}}. $$ If we take a pendulum where there is no gravitational field, then $g=0$, therefore the period should become infinity. In such a condition what will our time relative to that of a person on earth will be? I believe that the time of a person will become too slow as it takes infinite time to complete one oscillation. Please tell me whether I am right or wrong, and if I am wrong please help me understand why.
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4The infinite time period just indicates that the pendulum won't move at all. – Hritik Narayan Apr 29 '15 at 17:01
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3Just because a pendulum clock doesn't 'tick' in zero g doesn't mean that time stops. – Time4Tea Apr 29 '15 at 17:06
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1Adding to @Time4Tea's comment: does time stop when your watch runs out of battery? – AV23 Apr 29 '15 at 17:27
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The pendulum motion is caused by a restoring force whose whose tangential component is opposite to displacement in direction. The tension from the string, if any, would always be perpendicular to the path. When there is no such force to provide the restoring force, the type of oscillation you mentioned would not happen.
BTW, a kind reminder- Mathematics is powerful friend of Physics, and a reliable ally also, in most of the cases. (Just a metaphorical illustration LOL) To clearly understand a problem, perhaps it's best to start at the physics, instead of the mathematics, since the equations were derived for particular scenario (e.g. in the presence of certain fields), which might be fundamentally different from the scenario at hand.
user202531
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Please can u tell me what will be the relative time of a person experiencing no gravitational field to that of a person living on earth – Steffi Apr 30 '15 at 18:49
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In that place, where g=0. T goes to infity. What it means?, just that the pendulum will not move. Just that. The time will run normally in that place and in the earth.
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Example on time on earth running different from a satellite orbiting the earth as both of them experience different g. That is time goes little faster for satellite. – Steffi Apr 30 '15 at 18:53
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the time period in a SHM is related to the force causing the motion, the force which is proportional to the negative o the displacement. In the case of gravitational force, one simple example is that of the simple pendulum.T=2πLg−−√
