The frequency refers to the number of cycles per time lapse, while the period is the inverse of the frequency, therefore we would have this expression,
[tex]f= \frac{N}{t}[/tex]
Here,
N = Number of Cycles
t = Time
While at the same time Period is the inverse of the frequency, then
[tex]T = \frac{1}{f}[/tex]
Replacing,
[tex]T = \frac{1}{N/t}[/tex]
[tex]T = \frac{t}{N}[/tex]
Replacing we have that
[tex]T = \frac{144s}{109}[/tex]
[tex]T = 1.321s[/tex]
Gravity is one of the components that define the Period of a pendulum as well as its length, mathematically this expression is given as,
[tex]T = 2\pi \sqrt{\frac{l}{g}}[/tex]
[tex]g = \frac{4\pi^2l}{T^2}[/tex]
Replacing,
[tex]g = \frac{4\pi^2 (49*10^{-2}m)}{(1.321s^2)^2}[/tex]
[tex]g = 11.0853m/s^2[/tex]
Therefore the acceleration due to gravity of the planet is [tex]11.08m/s^2[/tex]
