UCSS Math II 5.9.5 Example 4
- Walch Education
The potential energy in joules of an oscillating spring can be represented by the expression , where is a constant and is the time in seconds since the spring began oscillating. Create a two-column proof to show that the potential energy of the spring can also be written as .
- Create the outline for the two-column proof.
- Rewrite the fraction on the left side of the equation as the difference of two fractions.
- Simplify .
- Use the reciprocal identity to rewrite the expression from step 3.
- Use the Pythagorean identity to rewrite the expression .
- Fill in the columns of the two-column proof.