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Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. y1 = r/2, y2 = r (for the two given position) Now, y1 = r sin ωt1 ⇒ r/2 = r sin ωt1 ⇒ sin ωt1 = 1/2 ⇒ ωt1 = π/2 ⇒ 2π/t × t1 = π/6 ⇒ t1 = t/12 Again, y2 = r sin ωt2 ⇒ r = r sin ωt2 ⇒ sin ωt2 = 1 ⇒ ωt2 = π/2 ⇒ (2π/t) t2 = π/2 ⇒ t2 = t/4 So, t2 – t1 = t/4 – t/12 = t/6

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