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# 3.1: Getting’ the Swing

Difficulty Level: At Grade Created by: CK-12

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

## Part 1 – Warm-up

In $y1$, enter $\cos(x)$. Press $F3$ and select 7: ZoomTrig. Use the graph to answer the following questions.

1. What is the range?

2. What is the amplitude? $A=$

3. What is the period? $T=$

Now change your calculator mode to split screen. Press 3 and select TOP-BOTTOM for Split Screen. For Split 1 App, select $Y=$ Editor. For Split 2 App, select Graph. In $y2$, enter an equation in the form $y = A \cdot \cos(B \cdot x) + C$, where $A$, $B$, and $C$ are integers. Press $2 + \alpha$ to swap applications to see the graph screen update. Press $2 + \alpha$ again to go back to the $Y=$ 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 $A$.

5. Describe the effect of increasing $C$.

6. Describe the effect of increasing $B$.

7. What is the relationship between $B$ and the period, $T$?

8. If a positive $D$ shifts the graph to the right $D$ units, what is the general sinusoidal equation for which this is true?

## 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, $D$, to the nearest tenth. If a motion detector is not available, use the lists 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:

$y=\\\\\\v=\\\\\\a=$

Confirm your position and velocity equations by graphing them. To confirm your position equation, enter your equation in $y1$ and select to show Plot 1 as shown to the right. To plot the velocity-time graph, use $L1$ for time and $L3$ for velocity. For the acceleration-time graph, use $L1$ for time and $L4$ for acceleration.

Feb 23, 2012

Nov 04, 2014