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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. `
3 years ago

396 Points
```										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

```
3 years ago
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