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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 -
(1) time period of oscillations is 8τ
(2) amplitude of motion is 4a
(3) time period of oscillations is 6τ
(4) amplitude of motion is 3a
- (1) time period of oscillations is 8τ
- (2) amplitude of motion is 4a
- (3) time period of oscillations is 6τ
- (4) amplitude of motion is 3a
Correct answer: (3) time period of oscillations is 6τ
Solution
The particle's distances traveled in successive time intervals indicate a quadratic relationship, characteristic of simple harmonic motion. The total distance covered suggests that the time period is 6τ, as the distances align with the expected behavior of a harmonic oscillator.
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