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Differentiati...

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Differentiation of omega t

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Q. The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
(a) y" + y' = 0
(b) y" − ω² y = 0
(c) y" = −ω² y
(d) y" + y = 0

ω

is a cube root of unity, then the value of determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + ω & ω^{2} & ω ω^{2} + ω & - ω & ω^{2} 1 + ω^{2} & ω & ω^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

Q. Assertion :Function

ε = a e^{- α x} cos (ω t - k x)

a, α, ω

k

are constants, represents a plane wave. Reason: Any differentiable function

f (t - α x)

provides a solution of wave equation.

1, ω, ω^{2}

are the three cube roots of unity,

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8})

...to 2n factors

=

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) . . . . . .

to 2n factors =

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