Question

Two pendulums of same amplitude but time period 3s and 7s start oscillating simultaneously from two opposite extreme positions. After how much time they will be in phase.

• A. $\frac{21}{8}s$
• B. $\frac{21}{4}$
• C. $\frac{21}{2}s$
• D. $\frac{21}{10}s$

Answer 1

The correct option is A $\frac{21}{8}s$

$y_1=acos{\omega }_{1}t$ and $y_2=acos(\pi +\omega t)$
For same phase ${\omega }_{1}t=\pi +{\omega }_{2}t$
$t=\frac{\pi }{{\omega }_1-{\omega }_2}=\frac{\pi }{\frac{2\pi }{3}-\frac{2\pi }{7}}=\frac{21}{8}s$