Question

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

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

Answer 1

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

Equation for pendulum can be considered as
$y_1=acos{\omega }_{1}t$ and $y_2=acos({\omega }_{2}t+\pi )$

For same phase ${\omega }_{1}t=\pi +{\omega }_{2}t$

$t=\frac{\pi }{{\omega }_1-{\omega }_2}=\frac{\pi }{\frac{2\pi }{3}-\frac{2\pi }{7}}=\frac{21}{8}\text{s}$

$\therefore \left(a\right)$