The period of the second pendulum is 0.9 s
Explanation:
The period of a simple pendulum is given by the equation
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where
L is the length of the pendulum
g is the acceleration of gravity at the location of the pendulum
For the first pendulum, we have
L = 0.64 m
T = 1.2 s
Therefore we can find the value of g at that location:
[tex]g=(\frac{2\pi}{T})^2 L=(\frac{2\pi}{1.2})^2 (0.64)=17.5 m/s^2[/tex]
Now we can find the period of the second pendulum at the same location, which is given by
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where we have
L = 0.36 m (length of the second pendulum)
[tex]g=17.5 m/s^2[/tex]
Substituting,
[tex]T=2\pi \sqrt{\frac{0.36}{17.5}}=0.9 s[/tex]
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