Answer Happy

Electrical Circuits Problem 2. The current I(t) in an RLC
circuit with voltage source E(t) is governed by the initial value
problem 10I ’’(t) + 80I ’ (t) + 410I(t) = e(t), I(0) = 2, I ’ (0) =
−8. where e(t) = E’ (t). Find a formula for the solution I(t) in
terms of e(t) using the Laplace transform technique and
convolution.
Electrical Circuits Problem 2. The current /(t) in an RLC circuit with voltage source Elt) is governed by the initial value problem ReR w Inductance 10'' (t) + 801(t) + 410/(t) = e(t), 7(0) = 2, 7(0) = -8. where e(t) = E (t). Find a formula for the solution /(t) in terms of e(t) using the Laplace transform technique and convolution. Capacita (5 points) Impulses and Dirac Delta Delta functions are also useful when representing point loads on a steel beam. Suppose we have a beam of length L, resting on two simple supports at the ends. The vertical deflection of the beam a distance x from the support is denoted by y(x). The deflection y(x) satisfies the Euler-Bernoulli equation , EI = F(x), where E, the elastic modulus, and I, the moment of inertia, are constants, and F(x) is the force applied per unit length at position x. If the beam has a concentrated load acting on it in the center of the beam, then the deflection must satisfy the symbolic boundary value problem: dy EI" = -F8(x - a), 'dx where x = a is the point where the mass is applied, F is the force applied and the minus sign indicates that the force is downward. The end points of the beam satisfy the conditions, y(0) = 0, y(L) = 0, y"0) = 0, y" (L) = 0.