Einföld hreintóna sveifla: diffurjafna Lausn á diffurjöfnunni fyrir SHM, einfalda hreintóna sveiflu A: amplitude, sveifluvídd ω: angular frequency,

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Presentation transcript:

Einföld hreintóna sveifla: diffurjafna

Lausn á diffurjöfnunni fyrir SHM, einfalda hreintóna sveiflu A: amplitude, sveifluvídd ω: angular frequency, horntíðni φ: phase angle, fasahorn ω = 2 π f = 2 π / T f: frequency, tíðni T: period, sveiflutími

A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. At point P, the mass has 1. positive velocity and positive acceleration. 2. positive velocity and negative acceleration. 3. positive velocity and zero acceleration. 4. negative velocity and positive acceleration. 5. negative velocity and negative acceleration. 6. negative velocity and zero acceleration.

A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. At point P, the mass has 1. positive velocity and positive acceleration. 2. positive velocity and negative acceleration. 3. positive velocity and zero acceleration. 4. negative velocity and positive acceleration. 5. negative velocity and negative acceleration. 6. negative velocity and zero acceleration.

Diffurjafna (SHM) md2x/dt2 = - kx

Mastering Physics: http://wps.aw.com/aw_young_physics_11 9.5 Ape Drops Tarzan

1 Hvort er 1 eða 2 sambærilegur? 2 3. æfing í verklegu

k = k1 + k2 k = k1 + k2 k = (k1k2) /(k1 + k2) 3. æfing í verklegu

Mastering Physics: http://wps.aw.com/aw_young_physics_11 9.8 One-and Two-Spring Vibrating Systems

Innri sveifla sameinda

Einfaldur pendúll

Diffurjafna: d2θ(t)/dt2 = - g/L sin θ(t)

Nálgun: sin θ = θ

Lausn: cosinus-fall með horntíðninni ω = √g/L

Raunpendúll:

T = 2π/ω ≈ √L v = S/T ≈ L/ √L = √L Univ.Phys. síðu 498

Þú rólar þér í rólu án þess að hreyfa þig, þ. e. a. s Þú rólar þér í rólu án þess að hreyfa þig, þ.e.a.s. þú fylgir eðlilegum sveiflum rólunnar. Svo stendur þú upp í rólunni, verður þá tíðni hinnar eðlilegu sveiflu: 1. meiri 2. sama 3. minni

Þú rólar þér í rólu án þess að hreyfa þig, þ. e. a. s Þú rólar þér í rólu án þess að hreyfa þig, þ.e.a.s. þú fylgir eðlilegum sveiflum rólunnar. Svo stendur þú upp í rólunni, verður þá tíðni hinnar eðlilegu sveiflu: 1. meiri 2. sama 3. minni Þú færir þyngdarpunktinn ofar, styttir svo að segja í pendúlnum, rólan sveiflast því hraðar!

Hvað af eftirfarandi er nauðsynlegt til að hlutur sveiflist: 1. stöðugt jafnvægi (stable equilibrium) 2. lítil eða engin mótstaða (little or no friction) 3. truflun (disturbance)

Allt þrennt! Stöðugt jafnvægi er nauðsynlegt. Í viðbót þarf truflun frá jafnvægisástandi til að koma hlutnum af stað. Að lokum þarf mótstaða að vera lítil því annars sveiflast hluturinn aðeins aftur í jafnvægispunkt án þess að sveiflast yfir hann.

Deyfð sveifla: Fx = - kx - bvx md2x/dt2 = - kx – bdx/dt

undirdeyfing, yfirdeyfing, markdeyfing

Þvinguð sveifla Þvingunarkraftur: F(t) = Fmaxcos(ωd t) Hámark þegar ωd = √k/m = ω Hermun, resonance