2. The length of time that it takes for a pendulum to make one complete swing depends on the length of the pendulum. The time in seconds, T, is related to the length in metres, L, through the equation T = 2π√(L/9.8)
c. Graph this function for pendulums up to 20m in length.
What equation would I have to input to come up with this graph? Thank you
To graph the function for pendulums up to 20m in length, you would need to input the equation T = 2π√(L/9.8) into a graphing tool or software. Different graphing tools or software may have slightly different syntax, but the general equation should remain the same.
Here's the step-by-step process to graph the function:
1. Set up the graphing tool or software: Open any graphing tool or software that allows you to input equations and create graphs. There are several online graphing tools available, such as Desmos, GeoGebra, or even Microsoft Excel.
2. Input the equation: In the equation or function input field of the graphing tool, enter T = 2π√(L/9.8). Note that some graphing tools may require adjustments to the equation syntax, such as using ^ for exponentiation or different symbols for math functions (e.g., sqrt() instead of √()).
3. Set the range for the length: In this case, you want to graph pendulums up to 20m in length. Find the input field or options that allow you to specify the range or domain for the independent variable, L. Set the range from 0 to 20.
4. Specify the axes: Make sure to label the x-axis as the pendulum length in meters (L) and the y-axis as the time in seconds (T).
5. Select the appropriate scale: Adjust the scale of the x-axis and y-axis, if needed, to allow for clear visualization of the graph. You may need to scale the axes differently depending on the values of the function.
6. Create the graph: Click on the "Graph" or "Plot" button, depending on the graphing tool you are using. This will generate the graph of the equation T = 2π√(L/9.8) for pendulums up to 20m in length.
By following these steps, you should be able to input the equation and create the graph for the given function.