Respuesta :
Answer:
L = 6.2 m
Explanation:
The angular velocity of a simple pendulum is
w = √ g / L
Where w is the angular velocity, g is the acceleration of gravity, which we assume 9.8 m / s2 and L is the length of the pendulum
Angular velocity, frequency and period are related
w = 2π f = 2 π / T
2π / T = √ g / L
L = g T² / 4π²
Let's calculate
L = 9.8 5²2 / 4π²
L = 6.2 m
Answer:
The simple pendulum must be 6.2 m to make one swing per five seconds.
Explanation:
The angular frequency of the simple pendulum is
[tex]\omega = \sqrt{\frac{g}{L}}[/tex]
The period of the pendulum is then
[tex]T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{L}{g}}[/tex]
The definition of the period is the time it takes to complete one cycle. So, it order the pendulum to complete one cycle in five seconds, then T = 5.
[tex]T = 2\pi \sqrt{\frac{L}{g}}\\\frac{L}{g} = (\frac{T}{2\pi})^2\\L = \frac{T^2g}{4\pi^2} = \frac{5^2(9.8)}{4\pi^2} = 6.2~m[/tex]
