Angular frequency of pendulum is given by
[tex]\omega = \sqrt{\frac{g}{l}}[/tex]
for both pendulum we have
[tex]\omega_1 = \sqrt{\frac{9.81}{1.00}}[/tex]
[tex]\omega_1 = 3.13 rad/s[/tex]
For other pendulum
[tex]\omega_2 = \sqrt{\frac{9.81}{1.1025}}[/tex]
[tex]\omega_2 = 2.98 rad/s[/tex]
now we have relate angular frequency given as
[tex\omega_1 - \omega_2 = 3.13 - 2.98 = 0.15 rad/s[/tex]
now time taken to become in phase again is given as
[tex]t = \frac{2\pi}{\omega_1 - \omega_2}[/tex]
[tex]t = \frac{2\pi}{0.15} = 41.88 s[/tex]
now number of oscillations complete in above time
[tex]N = \frac{t}{\frac{2\pi}{\omega_1}}[/tex]
[tex]N = \frac{41.88}{\frac{2\pi}{3.13}}[/tex]
[tex]N = 21 oscillation[/tex]
