KS5 Simple Harmonic Motion

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Simple Harmonic Motion Learning Objectives

Content

• Analysis of characteristics of simple harmonic motion (SHM).
• Condition for SHM: a ∝ − x
• Defining equation: a = − ω2x
• x = Acos ωt and v = ± ω √(A2 − x2)
• Graphical representations linking the variations of x, v and a with time.
• Appreciation that the v − t graph is derived from the gradient of the x − t graph and that the a − t graph is derived from the gradient of the v − t graph.
• Maximum speed = ωA
• Maximum acceleration = ω2A
• Study of mass-spring system: T = 2π √(m/k)
• Study of simple pendulum: T = 2π √(l/g)
• Questions may involve other harmonic oscillators (e.g. liquid in U-tube) but full information will be provided in questions where necessary.
• Variation of Ek, Ep, and total energy with both displacement and time.
• Effects of damping on oscillations.
• Qualitative treatment of free and forced vibrations.
• Resonance and the effects of damping on the sharpness of resonance.
• Examples of these effects in mechanical systems and situations involving stationary waves.

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