it is said that the time period of a simple pendulum in space is infinite. it is because the gravity in space is zero and anything divided by zero is equal to infinity.how can time period be infinite? also, in space, everything just floats around. how can a pendulum in space do oscillations if there is no restoring force to bring the mass back to mean position. how can a simple pendulum exhibit SHM in space? if it cannot exhibit SHM , how is the time period formula for the simple pendulum applicable to the pendulum in space and what is the meaning of infinite time period. why do the time period of pendulum in space even exists?
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The formula for the time pendulum at earth is given by $$T= 2\pi \sqrt{\frac lg}$$ which is valid only for constant values of $g$. On earth, even thought this is variable, we do usually consider it to be equal to, or around 9.8 $m/s^2$. However, there is no gravitational force acting on said pendulum in space- there is no restoring force that would try to bring back the bob of the pendulum back to it's initial position. Simply substituting $g=0$ in the equation for the time period will corroborate this statement- the infinite time period simply means that it would never come back to it's initial position- it is not oscillating or performing SHM since there is no restoring force to bring it back to it's initial equilibrium position.
