About This Chapter
Calculus Applications: Projectile & Harmonic Motion - Chapter Summary
This engaging chapter covers projectile and harmonic motion and other related calculus topics. Our instructors explain the definition of projectile motion in these lessons and then provide you with practice problems to test your knowledge. You'll also review simple harmonic motion (SMH), its formulas and definition. This chapter is designed to help you meet the following objectives:
- Explain the theory and equation associated with oscillation
- Define how pendulums are used in physics
- Solve problems involving simple harmonic motion
- Use differentiation to describe resultant motion
These helpful lessons have been created by professional instructors to make even the most challenging topics simple and user-friendly. Before moving on to other subjects, take the associated multiple-choice quiz that follows each lesson. If you need to review any of the material in a video lesson again, use the video tabs feature in the Timeline to skip directly to that section. Our instructors are available to help if you find that you need any assistance.
1. Projectile Motion: Definition and Examples
A projectile is any object that is given an initial velocity and then follows a path determined entirely by gravity. In this lesson, we will introduce projectile motion and touch on a few key facts to keep in mind when working through these problems.
2. Projectile Motion Practice Problems
After watching this video lesson, you will know how to use the sets of equations that are used to solve projectile motion problems. Learn how to manipulate them to find the answer you need.
3. Simple Harmonic Motion (SHM): Definition, Formulas & Examples
After watching this video, you should be able to explain what simple harmonic motion is, describe the features of the motion, and use equations to solve simple harmonic motion problems, particularly for a mass on a spring. A short quiz will follow.
4. Oscillation: Definition, Theory & Equation
In this article you will learn about mathematical functions that are used to model oscillations. An oscillation is any motion that repeats itself, and the function describing a particular oscillation is an example of a periodic function. Sine and cosine are the most common periodic functions.
5. Pendulums in Physics: Definition & Equations
After watching this lesson, you will be able to explain what a pendulum is, why it is an example of simple harmonic motion, and use equations to solve pendulum problems. A short quiz will follow.
6. Solving Simple Harmonic Motion Problems
In this lesson, you'll learn how we derive the displacement, velocity, and acceleration formulas for simple harmonic motion. You'll then use this knowledge to work through several simple harmonic motion problems yourself.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards