# UTPA STEM/CBI Courses/Physics (Calculus Based)/Oscillatory Motion

Course Title: Calculus Based Physics I

Lecture Topic: Oscillatory Motion

Instructor: Liang Zeng

Institution: University of Texas-Pan American

## Backwards Design[edit]

**Course Objectives**

**Primary Objectives**- By the next class period students will be able to:- Know the definitions of period, frequency, angular frequency (angular frequency is equivalent to angular speed – discussion of artificial unit radians – page 270 Serway)
- Know how to analyze the motion of an object attached to a horizontal spring in terms of displacement as a function of time
- Know how to analyze the motion of a pendulum in terms of displacement as a function of time

**Sub Objectives**- The objectives will require that students be able to:- text
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**Difficulties**- Students may have difficulty:- Understanding the derivation of displacement of a spring/pendulum as a function of time (2nd order differential equation)
- Understanding that x(t) = Acos(ωt + φ) (equation 15.6 page 420 Serway 7th edition) is representative and not the only way to express displacement; once initial conditions are given various representations are all valid and lead to the same result (eg. sine instead of cosine)
- Understanding what ω means

**Real-World Contexts**- There are many ways that students can use this material in the real-world, such as:- Springs – forces between atoms in solids (page 428 Serway 7th edition)
- Pendulum – grandfather clock

**Model of Knowledge**

**Concept Map**- text
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**Content Priorities****Enduring Understanding**- Definitions of period, frequency, angular frequency (angular frequency is equivalent to angular speed – discussion of artificial unit radians – page 270 Serway)
- Analyze the motion of an object attached to a horizontal spring in terms of displacement as a function of time
- Analyze the motion of a pendulum in terms of displacement as a function of time

**Important to Do and Know**- Analyze the kinetic and potential energy of simple harmonic oscillators (spring/pendulum) to determine velocity

**Worth Being Familiar with**- The physical and torsional pendulums
- Damped and forced oscillations

**Assessment of Learning**

**Formative Assessment**- In Class (groups)
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- Homework (individual)
- Pay attention to the following new units: s, Hz, s-1, rads
- Self-reading Sections Chapter 15: 15.1 – 15.5 (up to the physical pendulum) in the textbook
- (Motion of simple harmonic oscillator: Serway 7th edition page 441 #6). A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations.
- Find the period of its motion
- Find the frequency in hertz
- Find the angular frequency in radians per second

- (Energy of simple harmonic oscillator: Serway 7th edition page 442 #17). A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.00 cm.
- Find the total energy of the system when the position is 1.00 cm
- Find the speed of the object when the position is 1.00 cm
- Find the kinetic energy when the position is 3.00 cm
- Find the potential energy when the position is 3.00 cm

- (Motion of a pendulum: Serway 7th edition page 443 #28 a and b). A simple pendulum is 5.00 m long.
- What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2?
- What is its period if the elevator is accelerating downward at 5.00 m/s2?

- (Motion of simple harmonic oscillator: Serway 7th edition page 441 #6). A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations.

- In Class (groups)

**Summative Assessment**- text
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## Legacy Cycle[edit]

**OBJECTIVE**

By the next class period, students will be able to:

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The objectives will require that students be able to:

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**THE CHALLENGE**

Astronauts in space need to keep track of their weight as an indicator of their health while living on board the International Space Station. Design an apparatus based on the principles of simple harmonic motion for determining the mass of an astronaut on the International Space Station with zero weight. Give a hand-drawn schematic of the apparatus, describe how it works, and use equations to show how you would determine the mass based on measurable/observable parameters.

**GENERATE IDEAS**

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**MULTIPLE PERSPECTIVES**

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**RESEARCH & REVISE**

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**TEST YOUR METTLE**

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**GO PUBLIC**

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## Pre-Lesson Quiz[edit]

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## Test Your Mettle Quiz[edit]

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