Question

Two pendulums have time periods $T$ and $5T/4$. They start SHM at the same time from the mean position. After how many oscillations of the smaller pendulum will they be in same phase again?

• A. $5$
  
• B. $4$
  
• C. $11$
  
• D. $9$
  

Answer 1

Answer: (A)

$5$

When the pendulum $A$ with time period $\frac{5T}{4}$ completes phase of $2\pi$ in $\frac{5T}{4}$, the other pendulum $B$ leads by phase $\frac{\pi }{2}$.
So after $4$ oscillations of pendulum $A$ i.e. after $5T$, pendulum $B$ leads by $2\pi$ i.e they come in phase.
i.e. after $5$ oscillations of small pendulum $($ Time taken$=5T)$, they will again come in the same phase.