IB›IB Physics SL›Mind mapsC.1 Simple harmonic motionIB Physics SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is SHM?Acceleration ∝ displacement from equilibriumAcceleration always directed towards equilibriumRestoring force proportional to displacementPendulum works only for small anglesDefining equationa=−ω2xa = -\omega^2 xa=−ω2xMinus sign: acceleration opposes displacementTest: a/x constant and negativeamax=ω2x0a_{max} = \omega^2 x_0amax=ω2x0 at maximum displacementDescribing oscillationsAmplitude x0x_0x0: maximum displacementT=1f=2πωT = \frac{1}{f} = \frac{2\pi}{\omega}T=f1=ω2πPeriod independent of amplitude: isochronousSHMsimple harmonic motionTTTfffω\omegaωSprings, pendulumsSpring: T=2πmkT = 2\pi\sqrt{\frac{m}{k}}T=2πkmSpring period does not depend on gPendulum: T=2πlgT = 2\pi\sqrt{\frac{l}{g}}T=2πglPendulum period independent of bob massMeasure g: g=4π2lT2g = \frac{4\pi^2 l}{T^2}g=T24π2lEnergyMaximum displacement: speed zero, all potentialEquilibrium: speed maximum, all kineticDamping dissipates thermal energy, amplitude fallsExam tipsAcceleration is zero at equilibrium, speed is greatestQuadruple mass or length: period doubles