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  2. Mechanics Lecture Notes 1 Lecture 9: Simple harmonic motion ...

    www.damtp.cam.ac.uk/user/po242/pdfs/Mech2015/L9.pdf
    8 Oct 2015: x = A cos ωt B sin ωt a cos(ωt ϵ) Peiωt Qeiωt, (2). ... The solution isx = A cos ωt B sin ωt. Initially, x = a and ẋ = 0, so.
  3. Mathematical Tripos Part IA Michaelmas term 2015 Mechanics…

    www.damtp.cam.ac.uk/user/po242/pdfs/Mech2015/examples9.pdf
    8 Oct 2015: The other end,B, is fixed. The particle moves in a horizontal circle a distance d below B. ... cos θ,. where cos θ = d/l. 2 A particle rests at the top of a smooth sphere.
  4. Lopsided coatings of a visco-elastic fluid on a vertical fibre

    www.damtp.cam.ac.uk/user/hinch/talks/APSBoston2015.pdf
    18 Nov 2015: 2. z2h5 B. 2. θ2h5 = 0,. (curiously A α/6, but B β/80). ... t1/4. h(π) =1 cos L. t1/4. (K ((π L) cos L sin L.
  5. Standard Model Mathematical Tripos, Part IIIDr M B Wingate ...

    www.damtp.cam.ac.uk/user/wingate/Notes/StdM/sheet3.pdf
    23 Feb 2015: weak. charged current interaction). Given R(θ) =. (cos θ sin θsin θ cos θ. ), ... 4 cos θ. (2a2D v2a2D2. )},. where v = 2 sin2 θW 12,a = 12.
  6. A reciprocal theorem for boundary-driven channel flows

    www.damtp.cam.ac.uk/user/lauga/papers/111.pdf
    31 Dec 2015: ex. ez. ) a2 y(ez. ey eyez). (16). The contour of the elliptical cross section can be parameterized as x = a cos , y = b sin , with0   2. ... a sin e. x. b cos eypa2sin2 b2cos2. , n =b cos e.
  7. 7 Green’s Functions for Ordinary Differential Equations One of ...

    www.damtp.cam.ac.uk/user/dbs26/1BMethods/GreensODE.pdf
    9 Nov 2015: 87 –. while the jump condition gives. B( cos(1 ξ)) A cos ξ = 1. ... The generalsolution of this homogeneous equation c1 cos x c2 sin x and the inhomogeneous boundary.
  8. Instabilities of a thin coating on a vertical fibre; Newtonian,…

    www.damtp.cam.ac.uk/user/hinch/talks/Leeds2015.pdf
    10 Oct 2015: H′3 H′′′3 = G1. 1. Pn1 (1 cos x)n1, H3 Sx. ... H′5 H′′′5 = 0, H5 = A5 B5 sin x C5 cos x.
  9. Instabilities of a thin coating on a vertical fibre; Newtonian,…

    www.damtp.cam.ac.uk/user/hinch/talks/ICL2015.pdf
    4 Nov 2015: n 1)(n (n 1) cos x). (2n 1)(2n 1). xπ. 1. ... H′3 H′′′3 = G1. 1. Pn1 (1 cos x)n1, H3 Sx.
  10. 3 Laplace’s Equation In the previous chapter, we learnt ...

    www.damtp.cam.ac.uk/user/dbs26/1BMethods/Laplace.pdf
    26 Oct 2015: When λ 0 then X(x) = a sin(λx) b cos(. λx) solves X′′ = λX. ... λx B cos. λx, but if we impose the boundary condition y(1) = y(1) then.
  11. PHYSICAL REVIEW E 92, 023004 (2015) Phase-separation models for ...

    www.damtp.cam.ac.uk/user/lauga/papers/109.pdf
    4 Aug 2015: where. Vn = (An Bny)eny sin nξ (Cn Dny)eny cos nξ.(11). ... 3), is given by. rs = (δ ρ cos θ )x ρ sin θ y z z, δ = b sin k(z ct ),(18).
  12. Cop yrig ht © 201 3 U nive rsity ...

    www.damtp.cam.ac.uk/user/tong/em/macfarlane.pdf
    13 Jan 2015: repr. oduc. ed w. ithou. t per. mis. sion. In the last step, we used spherical polars with z = r cos θ. ... is. φ = a b. r. (90). Next we have solutions, like the dipole potential, cos θ,.
  13. Mathematical Methods University of Cambridge Part IB Mathematical…

    www.damtp.cam.ac.uk/user/dbs26/1BMethods/All.pdf
    30 Nov 2015: plex exponential eiθ = cos θ i sin θ. This is periodic with period 2π, and so we can view. ... f̂0. n=1. an cos nθ bn sin nθ. (1.14). 4Recalling that the orthonormal functions were {einθ/.
  14. The Standard Model

    www.damtp.cam.ac.uk/user/wingate/Notes/StdM/stdmodel.pdf
    2 Mar 2015: M AT T H E W B W I N G AT E. ... B = γ5C =. (iσ2 00 iσ2. ). (3.4.6). Then the Dirac field transforms as.

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