A simple pendulum suspended from the ceiling of a train has a period 'T' when the train is at rest. When the train is accelerating with a uniform acceleration, the time period of simple pendulum will:
Correct answer: A. Decrease
- A. Decrease
- B. Increase
- C. Remains unchanged
- D. Becomes infinite
Explanation
When the train accelerates horizontally, the pendulum experiences a net effective gravitational force given by geff= √(g² + a²), which is greater than the gravitational acceleration g. The time period of the pendulum, expressed as T = 2π√(L/geff), therefore results in a shorter period since geff > g and leads to faster oscillations.
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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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