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Solution: The product of the impulsive force and its duration is unity, and because of its brief duration, the pulse may be considered to approximate an impulse The measured response may then be taken as the system impulse response h(t), and we assumethat h(t)=e−3t (20) The response to a ramp in input force, F(t)=t for t>0, may be found by

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Solving convolution problems

Therefore, the solution is y(t) = ln(t+1)u(t) Example 3: pulse input, unit step response Let x(t) = u(t) – u(t–2), h(t) = u(t) The integrand is zero when τ < 0 and τ > 2, so that at most the integrand is non-zero when 0 < τ < 2 It is also zero when τ > t This sets up three intervals for t First, when t < 0 there

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Equation produit nul avec identité r

C’est né gatif, pas zéro Ainsi, l’équation x2 - x - 1 - 0 n’a pas de solution dans Rb) - x2 - x 30 - 0 - cette équation est de 2 degrés; sa discrimination est '12 - 4 (-30) '121;' est positive pas zéro, et est carré 11 So équation - x2 ' x '30 '0 admet 2 solutions dans RCalcul ces solutions: donc équation - x2 x '30 ' 0 a pour