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A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then:
- amplitude of motion is 3a
- time period of oscillations is 8τ
- amplitude of motion is 4a
- time period of oscillations is 6τ
Correct answer: time period of oscillations is 6τ
Solution
The particle's motion is characterized by its displacement over time, and the distances traveled in successive intervals suggest a specific relationship between time and distance in simple harmonic motion. Given that the distances traveled are in a ratio of 1:2, this indicates that the total distance covered in the first two intervals corresponds to a complete cycle, leading to the conclusion that the time period of oscillations is 6τ.
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