Answer :
From the calculation, the gravitational field at the pendulum’s location is 9.8 m/s^2
What is a pendulum?
A pendulum is a device that is used to demonstrate oscillatory motion. We have the following information.
l = 36.9 cm or 0.369 m
T = 1.22 s
Then;
T = 2π√l/g
T/2π = √l/g
(T/2π)^2 = l/g
g(T/2π)^2 = l
g = l/(T/2π)^2
g = 0.369/(1.22/2 *3.14)^2
g = 9.8 m/s^2
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The gravitational field at the pendulum's location, calculated using the formula for the period of a simple pendulum, is approximately [tex]9.82 m/s^2.[/tex]
To calculate the gravitational field at the pendulum's location, we can use the formula for the period of a simple pendulum, which is given by:
[tex]T = 2\pi \sqrt{} (L/g)[/tex]
Here, T is the period, L is the length of the pendulum, and g is the gravitational field (or acceleration due to gravity). The goal is to solve for g, so we rearrange the formula to:
[tex]g = (4\pi ^2 * L) / T^2[/tex]
Substituting the given values into the equation:
L = 36.9 cm = 0.369 m (since g is typically in m/s² we convert length to meters)
T = 1.22 s
[tex]g = (4\pi ^2 * 0.369 ) / (1.22 s)^2[/tex]
After performing the calculation:
g = [tex]9.82 m/s^2.[/tex]
Therefore, the acceleration due to gravity at the location of the pendulum is approximately [tex]9.82 m/s^2.[/tex]