If the length of a seconds pendulum is quadrupled, how does its time period change________________?
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Answer: D. 2 times
Explanation
The time period of a simple pendulum is directly proportional to the square root of its length. Quadrupling the pendulum length multiplies the length value by a factor of four. Taking the square root of four yields a time period increase factor of two. A seconds pendulum has a standard period of exactly two seconds for one complete oscillation. Pendulum period formulas depend on string length and local gravitational acceleration. Mass does not affect the time period of an ideal simple pendulum oscillation.
Pendulum principles are used in mechanical grandfather clocks to maintain accurate timekeeping. Geologists use pendulum variations to measure subtle differences in local gravitational fields. Understanding square root scaling laws helps engineers analyze harmonic oscillator systems. Four times would occur if the time period scaled linearly with length without taking a square root. Six times represents an incorrect calculation outcome unrelated to pendulum length scaling laws. Eight times would imply a cubic or improper mathematical relationship for pendulum motion.
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