Final answer:
To determine the length of a simple pendulum with a 2-second period, use the formula T = 2π √(L/g). For Earth's gravity of 9.81 m/s², the calculation yields a pendulum length of approximately 0.991 meters.
Step-by-step explanation:
To find the length of a simple pendulum that has a period (T) of 2 seconds, we use the formula for the period of a simple pendulum: T = 2π √(L/g), where L is the pendulum's length and g is the acceleration due to gravity. Assuming Earth's standard gravity of 9.81 m/s², we rearrange the formula to solve for L: L = g∙(T/2π)². Let's plug in the values: L = (9.81 m/s²)∙(2 s/2π)².
To calculate:
First, divide the period by 2π: (2 s/2π) = 0.318 s.
Next, square this result: (0.318 s)² = 0.1011 s².
Finally, multiply this by g: 0.1011 s² ∙ 9.81 m/s² = approximately 0.991 m.
Therefore, the length of the pendulum should be approximately 0.991 meters for it to have a 2-second period.