In case the sound from the engine of a vehicle is modelled by the function  y(t) = cos[ω(t + τ) + θ]  where time delay=τ & phase=θ  Determine the frequency & period  of the signal u(t) when a)[ω, τ, θ] = [π/3, 1/2, π/2] b)[ω, τ, θ] = [3π/4, 1/2, π/4] N.b time should be in seconds & frequency in Hertz. c) y(t) = e-atu(t) for t≥0 & y(t) = 0 for t<0 where a>0 is a constant The function above defines the model of  the decay of the vibration of a vehicle engine. i.Make a sketch of the signal y(t) & determime its fourier transform.

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In case the sound from the engine of a vehicle is modelled by the function 
y(t) = cos[ω(t + τ) + θ] 
where time delay=τ & phase=θ 
Determine the frequency & period  of the signal u(t) when
a)[ω, τ, θ] = [π/3, 1/2, π/2]
b)[ω, τ, θ] = [3π/4, 1/2, π/4]

N.b time should be in seconds & frequency in Hertz.

c) y(t) = e-atu(t) for t≥0 & y(t) = 0 for t<0 where a>0 is a constant

The function above defines the model of  the decay of the vibration of a vehicle engine.

i.Make a sketch of the signal y(t) & determime its fourier transform.

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