# 3.1: Getting’ the Swing

**At Grade**Created by: CK-12

*This activity is intended to supplement Calculus, Chapter 2, Lesson 4.*

## Part 1 – Warm-up

In \begin{align*}y1\end{align*}**7: ZoomTrig**. Use the graph to answer the following questions.

1. What is the range?

2. What is the amplitude? \begin{align*}A=\end{align*}

3. What is the period? \begin{align*}T=\end{align*}

Now change your calculator mode to split screen. Press 3 and select **TOP-BOTTOM** for **Split Screen**. For **Split 1 App**, select \begin{align*}Y=\end{align*}**Editor**. For **Split 2 App**, select **Graph**. In \begin{align*}y2\end{align*}**Editor** to modify your equation. To answer the following questions, modify the corresponding variable to observe the changes each variable has to the equation.

4. Describe the effect of increasing \begin{align*}A\end{align*}

5. Describe the effect of increasing \begin{align*}C\end{align*}

6. Describe the effect of increasing \begin{align*}B\end{align*}

7. What is the relationship between \begin{align*}B\end{align*}

8. If a positive \begin{align*}D\end{align*}

## Part 2 – Collect & Analyze Data

You will collect data of a pendulum swinging. Using the skills reviewed in the warm-up, write a cosine function that models the data collected. Estimate the amplitude and period and phase shift, \begin{align*}D\end{align*}*time, distance*, and *velocity* from your teacher and graph a function to model that data. To collect data, complete the following steps:

- Using an I/O cable, connect the motion detector to the graphing calculator.
- On the
**HOME**screen, run the*Ranger*program. Select**1:Setup/Sample….**Use the settings that appear to the right and press**ENTER**. - Position the motion detector so that it is facing the pendulum, swing the pendulum, and press
**ENTER**to begin collecting data.

- If your data doesn’t look sinusoidal, press
**ENTER**and select**3:Repeat Sample**to repeat the trial. Then press**ENTER**to begin collecting data again. - Model the distance-time data with a function. Derive the velocity and acceleration equations. Select
**7:Quit**when you are finished.

Record your position, velocity and acceleration equations for your experiment data here:

\begin{align*}y=\\
\\
\\
v=\\
\\
\\
a=\end{align*}

Confirm your position and velocity equations by graphing them. To confirm your position equation, enter your equation in \begin{align*}y1\end{align*}