π Key Concepts
Periodic and oscillatory motionSimple Harmonic Motion (SHM)Amplitude, frequency, period, phaseDisplacement, velocity, acceleration in SHMEnergy in SHM (kinetic and potential)Simple pendulumSpring-mass systemAngular SHMDamped and forced oscillationsβ
π― Key Formulas
Period: T = 2Οβ(l/g) (pendulum), T = 2Οβ(m/k) (spring)Displacement: x = A cos(Οt + Ο)Velocity: v = -AΟ sin(Οt + Ο)Acceleration: a = -AΟΒ² cos(Οt + Ο)Angular frequency: Ο = 2Οf = 2Ο/TTotal energy: E = (1/2)kAΒ² = constantSpring constant: k = F/xAngular SHM: ΞΈ = ΞΈβ cos(Οt + Ο)β
β οΈ Common Mistakes to Avoid
Confusing amplitude and displacementWrong signs in velocity/accelerationIncorrect phase calculationsMixing up angular and linear quantitiesForgetting initial conditionsWrong energy calculationsβ
π Knowledge Prerequisites
- Trigonometry
- Basic calculus (derivatives)
- Vector concepts
- Newton's laws
- Energy concepts
- Circular motion
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π‘ Tips for Students
Understand the connection between circular and SHMLearn to sketch displacement, velocity, acceleration graphsPractice phase difference problemsMaster energy conservation in SHMUnderstand damping effectsConnect theory with real oscillatorsβ
π Practice Recommedations
Calculate periods and frequenciesSolve phase difference problemsDetermine velocity and acceleration at different pointsWork on energy conservation problemsAnalyze simple pendulum motionSpecial Notes:
- SHM is the projection of uniform circular motion
- Force is always towards mean position
- Energy oscillates between KE and PE
- Phase determines initial conditions
- Real oscillations always have some damping
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