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Created with Fabric.js 1.4.5 HEAVISIDE FUNCTION mathematical function denoted Mathematical function denoted H(x), or sometimes u(x) Known as "unit step function" The term "Heaviside step function" and its symbol can represent either a piecewise constant function or a generalized function. sin (t), 0 t < 6Write h(t) = 0, 6 t in terms of the Heaviside function. All functions start o. (this space left blank) At t = 0 we turn on sin(t) sin(t)U (t 0) At t = 6 we turn o sin(t) sin(t)U (t 6) Do nothing else (this space left blank)h(t) = sin(t)U (t 0) sin(t)U (t 6) (then we x notation) 0, 0 t < 1Write g(t) = cos(4t), 1 tin terms of the Heaviside function. All functions start o. (this space left blank) At t = 1 we turn on cos(4t) cos(4t)U (t 1) (We never turn o cos(4t)) (this space left blank) 5t 11, 0 t < 6 sin(3t), 6 t < 7Write ρ(t) = 4, 7 t < 12 t, 12 tin terms of the Heaviside function. All functions start o. At t = 0 we turn on 5t 11 (5t 11)U (t 1) At t = 6 we turn o 5t 11 and turn on sin(3t) (5t 11)U (t 6) + sin(3t)U (t 6) At t = 7 we turn o sin(3t) and turn on 4 sin(3t)U (t 7) + 4U (t 7) At t = 12 we turn o 4 and turn on t 4U (t 12) + tU (t 12) (We never turn o t) ρ(t) = (5t 11)(1) (5t 11)U (t 6) + sin(3t)U (t 6) sin(3t)U (t 7) + 4U (t 7) 4U (t 12) + tU (t 12) h(t) = sin(t)(1) sin(t)U (t 6) g(t) = cos(4t)U (t 1) GROUP 1
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