Applications of Calculus to Mechanics

In this module of Maths Extension 2, you will learn how problems in mechanics can be studied through the application of mathematical techniques related to vectors and calculus. You will learn how Newton's Laws of Motion can be applied to a variety of problems in mechanics to construct differential equations, whose solutions can then be used to produce insightful conclusions about the motion within these scenarios.

Simple harmonic motion

In this section you will learn about simple harmonic motion, which describes a periodic oscillation. You will learn how to identify when a motion is a simple harmonic osillator, and how to calculate the equations describing the position, velocity or acceleration at each point in time.

Modelling motion without resistance

In this section you will learn how to apply Newton's Laws of Motion to more complicated problems where forces and acceleration may change over time or where multiple forces are acting on an object.

Resisted motion

In this section you will learn how to apply Newton's Laws of Motion to scenarios where a resistive force is present which opposes the motion and grows with the speed of the motion. For objects that are moving under the influence of gravity and a resistive force, you will learn how to determine an object's terminal velocity, which is the fastest speed it can achieve in its motion.

Projectiles and resisted motion

In this section you will learn how to apply Newton's Laws of Motion to scenarios where a projectile is moving under the influence of both gravity and a resistive force after being launched. You will learn how to solve problems where the parameters of the launch are unknown or to be determined based on some criteria of the objects motion.

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