O Consider a single-degree-of-freedom overdamped system, which is harmonically excited by a forcing function of form F (t) = Fo sin wt. Express the equation of motion and solve it by finding the particular and homogeneous solutions given the initial conditions x (0) i (0) = vo⋅ = x0 and

A 225kN test aircraft moving with velocity v = Xo = 25 km/h collides with a rigid barrier at t = 0. As a result of the behaviour of its energy absorbing capabilities, the response of the aircraft to the collision can be simulated by the damped spring- mass oscillator shown with k = 3MN/m and c = 840 kN. s/m. Assume that the mass is moving to the left with a velocity vo = xo = 25 km/h and the spring is unstretched at t = 0 determine the aircraft's deceleration: a) Immediately after it contacts the barrier; b) att = 0.04s and; c) at t= 0.08s. Vo = ******** xo ****** Vo = xo www m Figure Q5 - Aircraft Collision F(t)

Obtain the state model for the two-mass system whose equations of motion are m₁x₁ + k₁(x₁ − x₂) = f(t) m₂x₂ − k₁ (x₁ - x₂)+k₂x₂ = 0

4- The logarithmic decrement can be obtained as & In*, is it possible to get a negative value of 8 when the system is damped (3 < 1)? Why?

The location h of a mass m on the end of a spring with a dampening factor k at time t is described by the following differential equation: m 2²h at² What type of variables are h, m, k, and t? + kh= 0

Consider the two-mass system shown below. The system is free to move in the x₁ - x₂ plane. 1. Obtain the FBD 2. Obtain the EOM 3. Using Modal Analysis, obtain the response of the system x2 X4 3k 4k 4k quing m m=10kg, k = 100 N/m m k 2k m 4k

8.6 Obtain the total response of the following models. 6x + 5x = 20u,(t), x(0) = 0 b. 6x + 5x = 20u, (t), x(0) = 1 a. C. 13x − 6x = 18u, (t), x(0) = −2 -

Identify the expression for the natural frequency of the system shown in the figure.