JEE Main 20146 April
- Exam
- JEE Main
- Year
- 2014
- Date
- 6 April
- Subject
- Physics
- Chapter
- Oscillations
JEE Main 2014 · 6 April · Physics · Oscillations
A particle moves with simple harmonic motion in a straight line. In...
A particle moves with simple harmonic motion in a straight line. In first , after starting from rest it travels a distance a, and in next it travels 2a, in same direction, then :
Options
- AAmplitude of motion is 3a
- BTime period of oscillations is 8 τ
- CAmplitude of motion is 4a
- DTime period of oscillations is 6 τ
Correct answer
D. Time period of oscillations is 6 τ
Step-by-step solution
...(i)
...(ii)
∴ - 1 + \dfrac{\text{a}}{\text{A}} = - \text\cos \omega τ ...(iii)
and - 1 + \dfrac{3 \text{a}}{\text{A}} = - \text\cos \left(2 \omega τ\right) ...(iv)
Adding (iii) and (iv)
2 = 3 \cos \left(\omega τ\right) - 2 {\text\cos}^{2} \left(\omega τ\right) + 1
∴ 2 {\text\cos}^{2} \left(\omega τ\right) - 3 \text\cos \left(\omega τ\right) + 1 = 0
∴ \text\cos \omega τ = \dfrac{1}{2}