Question

Two oscillating simple pendulums with time periods $T$ and $\frac{5T}{4}$ are in phase at a given time. They are again in phase after an elapse of time

• A. $4T$
• B. $3T$
• C. $6T$
• D. $5T$
• E. $8T$

Answer 1

The correct option is D $5T$

Let $1st$ pendulum have phase as $cos\left(2\pi t/T\right)t$ and and $2nd$ pendulum have $cos(2\pi t\times 4/5T)$ i.e $cos\left(8\pi t/5T\right)$, let they have same phase after time $t$.
So, we have
$cos\left(2\pi t/T\right)=cos(8\pi t/5T+2\pi )$
$2\pi t/T=8\pi t/5T+2\pi$
$0.4t/T=2$
$t=5T$