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Write in an essay format on the given topic with diagrams and needs to include many scientific reference sources and have intermediate level of detail.
Three particles A, B and C lie in that order in a straight smooth groove so that they can only move along the x-axis. Both A and C are of unit mass whilst B is of mass M. Particle B is joined to the other two by identical linear springs of unit stiffness.
(a) If the three particles are displaced from equilibrium by distances x1, x2 and x3 show that the equations of motion are
d2x1/dt2 = x2 - x1,
M d2x2/dt2 = x3 - 2x2 + x1,
d2x3/dt2 = x2 - x3.
(b) Prove that the frequencies of the three normal modes are given by ? = 0, 1 and ?2 = 1 + (2/M).
[5 marks]
(c) Describe the motions of the particles corresponding to the normal modes.[4 marks]
A meta analysis describing about the health effects on various individuals due to the exposure of electronic cigarette vapour.
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