Find the period of a pendulum that is 3 meters long if the period, T, of a pendulum in seconds can be found using the formula T = 2pi(square root L/9.8
find it for 2.5 meters as well.
Would love to see the work, not just the answer.
thank you.
To find the period of a pendulum using the given formula, we need to substitute the length (L) of the pendulum into the formula and solve for T.
Let's start with the pendulum length of 3 meters:
Given:
Length of pendulum (L) = 3 meters
Acceleration due to gravity (g) = 9.8 m/s^2
Formula:
T = 2π √(L / g)
Substituting the values into the formula:
T = 2π √(3 / 9.8)
Now, we can simplify this expression:
T = 2π √(0.306122)
Taking the square root:
T = 2π * 0.553972
Now, multiply and simplify to obtain the period:
T ≈ 3.477
Therefore, the period of a pendulum with a length of 3 meters is approximately 3.477 seconds.
Now, let's do the same for a pendulum with a length of 2.5 meters:
Given:
Length of pendulum (L) = 2.5 meters
Acceleration due to gravity (g) = 9.8 m/s^2
Formula:
T = 2π √(L / g)
Substituting the values into the formula:
T = 2π √(2.5 / 9.8)
Now, we can simplify this expression:
T = 2π √(0.255102)
Taking the square root:
T = 2π * 0.505074
Now, multiply and simplify to obtain the period:
T ≈ 3.175
Therefore, the period of a pendulum with a length of 2.5 meters is approximately 3.175 seconds.
Remember to always substitute the given values into the formula and simplify the expression step by step to find the final answer.