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Show that x(t) =c1cosωt+c2sinωt, (1) x(t) =Asin (ωt+φ), (2)   and x(t) =Bcos (ωt+ψ)   (3) are all...

Show that

x(t) =c1cosωt+c2sinωt, (1)

x(t) =Asin (ωt+φ), (2)   and x(t) =Bcos (ωt+ψ)   (3)

are all solutions of the differential equation d2x(t)dt2+ω2x(t) = 0. Show that thethree solutions are identical. (Hint: Use the trigonometric identities sin (α+β) =sinαcosβ+ cosαsinβand cos (α+β) = cosαcosβ−sinαsinβto rewriteEqs. (2) and (3) in the form of Eq. (1). To get full marks, you need to show the connection between the three sets of parameters: (c1,c2), (A,φ), and (B,ψ).)

From Quantum chemistry By McQuarrie

Science   Advanced-Physics   
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