If the length of a simple pendulum is increased four times, its frequency:
Correct answer: E. Decreases 2 times
- A. Increases 2 times
- B. Decreases 4 times
- C. Remains the same
- D. Increases 4 times
- E. Decreases 2 times
Explanation
The frequency of a simple pendulum is determined by the formula f = 1/2π√(g/L), which shows that the frequency is inversely proportional to the square root of the pendulum's length.When the length L is quadrupled, the new length is 4L. The new frequency is f' = 1/2π√(g/4L) = 1/2√4 × 1/2π√(g/L) = f/2.This means the frequency decreases by a factor of 2. Thus, Option E is correct.Other options are incorrect because they do not reflect the inverse square root relationship between frequency and length in a pendulum.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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