Unit 7 · 7.3 — Representing and Analyzing SHM

Everything to learn here

• Concept: The position, velocity, and acceleration of a perfect SHM oscillator can be accurately modeled by sinusoidal (sine and cosine) functions of time.
• Concept: When the oscillator passes through the zero position (equilibrium), its restoring force and acceleration are exactly zero, while its velocity is at its absolute maximum.
• Concept: When the oscillator's position is at its maximum (the amplitude), its velocity is exactly zero, and its acceleration and restoring force are at their absolute maximums.
• Equation: $$x(t)=A\cos (2\cdot \pi \cdot f\cdot t)orx(t)=A\cos (\omega \cdot t)\text{(Position mathematically defined as a function of time)}$$
• Vocabulary: Equilibrium Position — The natural resting coordinate point where the net force, restoring force, and acceleration are strictly zero
• Skill: Translation Between Representations — Given a position-time cosine graph, accurately sketching the corresponding velocity-time (sine) and acceleration-time (negative cosine) graphs, preserving period and phase shifts (90 and 180 degrees)
• Skill: Explain how position, speed, and rate of change of velocity vary throughout a cycle of simple harmonic motion.
• Equation: $$Usex=A\cdot \cos (2\cdot \pi \cdot f\cdot t)tomodelpositionandidentifywherevelocityandaccelerationreachtheirmaximumorzerovalues.$$
• Skill: Extract physical properties like amplitude and period by analyzing graphs of an object's motion over time.

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