The equation: T= 2* pi* sqrt(2/3L/9.8) Solve for L. Please show the solution step by step. The square root is giving me trouble in my solution. Thanks for your help.
If L is known:
1. Plug-in the value of L.
2. Simplify the quantity under the radical.
3. Take the square root of the number
under the radical.
Example:
L = 19.6 m.
Solve for T.
T = 2pi*sqrt((2/3)*L/g)
T = 6.28*sqrt((2/3)*19.6/9.8) =
6.28*sqrt((2/3)*2) = 6.28*sqrt((4/3) =
6.28 * 1.1547 = 7.25 s.
Freq. = 1/T Hz.
To solve the equation T = 2π√(2/3L/9.8) for L, we need to isolate L on one side of the equation. Here are the steps to solve it:
1. Start with the given equation: T = 2π√(2/3L/9.8).
2. Square both sides of the equation to eliminate the square root: T^2 = (2π√(2/3L/9.8))^2.
3. Simplify the right-hand side of the equation: T^2 = 4π^2 * (2/3L/9.8).
4. Distribute the squared term: T^2 = (4π^2 * 2/3L/9.8).
5. Simplify the fraction on the right side: T^2 = (8π^2/29.4L).
6. Multiply both sides of the equation by (29.4L) to isolate L: L = (8π^2/29.4) * T^2.
7. Divide the right-hand side by 29.4: L = (8π^2 * T^2)/29.4.
So, the solution for L is L = (8π^2 * T^2)/29.4.