Lesson Notes By Weeks and Term v4 - SHS 3
KINEMATICS
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KINEMATICS
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Subject: Physics
Class: SHS 3
Term: 1st Term
Week: 12
Grade code: 3.1.2.LI.2
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.1
Indicator code: 3.1.2.LI.2
Theme: MECHANICS AND MATTER
Subtheme: KINEMATICS
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This lesson explores the mathematics behind oscillatory motion, specifically Simple Harmonic Motion (SHM). SHM is a special type of periodic motion that is fundamental to understanding waves, sound, light, and many engineering systems. In our daily lives in Ghana, we see examples of this motion everywhere: a child on a swing (`abobɔn`) at the park, the vibration of a guitar string, or the way a car's suspension system bounces after hitting a pothole on the road. By understanding the kinematics of SHM, we can precisely describe and predict the position, speed, and acceleration of oscillating objects, which is crucial for fields like engineering, music, and technology.
A. Recap: The Foundation of SHM
Before we discuss velocity and acceleration, we must remember the defining condition of Simple Harmonic Motion: A body performs SHM if its acceleration (`a`) is directly proportional to its displacement (`x`) from a fixed equilibrium position, and is always directed towards that position.
Mathematically, this is expressed as: `a ∝ -x` `a = -ω²x`
Where: `a` is the acceleration. `x` is the displacement from the equilibrium position. `ω` (omega) is the angular frequency, a constant for the specific oscillating system. It is related to the period `T` and frequency `f` by `ω = 2π/T = 2πf`. The negative sign is crucial: it shows that the acceleration is always in the opposite direction to the displacement (i.e., it's a restoring force). B. Equation for Displacement (x)