Chapter 7, Problem 17QAP

Using simulation in MATLAB and show the results signal.

6. Consider a 10N step input to the mechanical system shown below, take M = 15kg, K = 135N/m, and b = 0.4 Ns/m. (a) Assume zero initial condition, calculate the (i) System pole (ii) System characterization, and (iii) The time domain response (b) Calculate the steady-state value of the system b [ www K 个 х M -F(+)

2. Solve the following linear time invariant differential equations using Laplace transforms subject to different initial conditions (a) y-y=t for y(0) = 1 and y(0) = 1 (b) ÿ+4y+ 4y = u(t) for y(0) = 0 and y(0) = 1 (c) y-y-2y=0 for y(0) = 1 and y(0) = 0

3. For the mechanical systems shown below, the springs are undeflected when x₁ = x2 = x3 = 0 and the input is given as fa(t). Draw the free-body diagrams and write the modeling equations governing each of the systems. K₁ 000 K₂ 000 M₁ M2 -fa(t) B₂ B₁ (a) fa(t) M2 K₂ 000 B K₁ x1 000 M₁ (b)

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1. Create a table comparing five different analogous variables for translational, rotational, electrical and fluid systems. Include the standard symbols for each variable in their respective systems.

An elliptically polarized wave traveling in -ve z-direction is received by circularly polarized antenna. 11 the unit vector of the incident wave is w = wave would be right hand CP. 2âx-jay. Find PLF (dimensionless) when the transmitted

2) Suppose that two unequal masses m₁ and m₂ are moving with initial velocities v₁ and v₂, respectively. The masses hit each other and have a coefficient of restitution e. After the impact, mass 1 and 2 head to their respective gaps at angles a and ẞ, respectively. Derive expressions for each of the angles in terms of the initial velocities and the coefficient of restitution. m1 m2 8 m1 m2 β

An elliptically polarized wave traveling in the negative z-direction is received by a circularly polarized antenna. The vector describing the polarization of the incident wave is given by Ei= 2ax + jay .Find the polarization loss factor PLF (dimensionless and in dB) when the wave that would be transmitted by the antenna is (a) right-hand CP (b) left-hand CP.