6.2.1 oscillations - wordpress.com · the simple pendulum and the mass on a spring (spring...

© 2016 flippedaroundphysics.com 6.2.1 Oscillations Oscillations are movements back and forth in a repeating pattern. Two examples are the simple pendulum and the mass on a spring (spring pendulum). Pendulum (1)! Sketch the displacement of the bob (from equilibrium) with time. (2)! What mathematical function could be used to describe this graph? Mass on a spring The mass oscillates up and down in a repeating pattern. (3)! Sketch a graph of the displacement of the mass from the equilibrium position against time. (4)! Mark on your graph the period of the oscillation. Label it T. (5)! At what points would the mass be moving fastest? Mark on the graph where this would occur. Label it v max . (6)! On the graph, above, mark on the amplitude of the oscillation (label it A), and describe what amplitude is. displacement time k displacement time

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6.2.1OscillationsOscillationsaremovementsbackandforthinarepeatingpattern.Twoexamplesarethesimplependulumandthemassonaspring(springpendulum).

Pendulum

(1)!Sketchthedisplacementofthebob(fromequilibrium)withtime.

(2)!Whatmathematicalfunctioncouldbeusedtodescribethisgraph?

Massonaspring

Themassoscillatesupanddowninarepeatingpattern.

(3)!Sketchagraphofthedisplacementofthemassfromtheequilibriumpositionagainsttime.

(4)!Markonyourgraphtheperiodoftheoscillation.LabelitT.

(5)!Atwhatpointswouldthemassbemovingfastest?Markonthegraphwherethiswouldoccur.Labelitvmax.

(6)!Onthegraph,above,markontheamplitudeoftheoscillation(labelitA),anddescribewhatamplitudeis.

displacemen

time

displacemen

time

Angularfrequency

Angularfrequencyisdefinedas:

𝜔 =2𝜋𝑇 = 2𝜋𝑓

Theunitsareradianspersecond(rads-1).

(7)!Ifaparticularoscillatoroscillateswithaperiodof0.125s,whatistheangularfrequency?

(8)!Describewhatyouthinkangularfrequencyrepresents.

PhaseDifference

Youhavecomeacrossphasedifferencebeforeinthetopicofwaveinterference.Phasedifferenceisanangle,andrepresentstheangulardifferencebetweentwooscillationswiththesamefrequency.

Phasedifferencecanbeexpressedasanangleindegreesorinradians.

(9)!Sketchwaveswhichhaveaphasedifferenceofi)90°,ii)π/8rad

3.0 Examples of chaotic systems - Richard C. Harkness · 3.0 Examples of chaotic systems Outline 3.1 Double pendulum 3.2 Magnetic Pendulum 3.3 Lorenz waterwheel 3.4 Planets 3.5 Spring/mass

§6.2.1 角

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