P= 2PI sqrt(L/g)
2.00=2PI sqrt(l/9.8) solve for L
2.00=2PI sqrt(l/9.8) solve for L
T = 2π√(L/g)
where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity which is approximately 9.8 m/s² on Earth.
Given:
L = 1.25 m
T = 2.00 s
g = 9.8 m/s²
We can rearrange the formula to solve for the square of the period:
T² = (4π²/g) * L
Now, let's substitute the given values and solve for the unknown position of the mass:
(2.00 s)² = (4π²/9.8 m/s²) * 1.25 m
4.00 s² = (4π²/9.8 m/s²) * 1.25 m
Multiplying both sides by (9.8 m/s²):
(9.8 m/s²) * 4.00 s² = 4π² * 1.25 m
39.2 m/s² * s² = 4π² * 1.25 m
Dividing both sides by (4π²):
(39.2 m/s² * s²) / (4π²) = 1.25 m
9.9 m = 1.25 m
To find the distance from the top of the pendulum, we subtract 1.25 m from the length of the pendulum:
Distance = 1.25 m - 1.25 m
Distance = 0 m
Therefore, the mass must be placed at the top of the pendulum (0 meters from the top) to give a period of 2.00 seconds.