Calculate the response of the system modeled by the equation (units are in Newtons): 5x + 125x = 108(t-n) Xo = 1 m, vo = -5 m/s

2. Use the following figure to construct a model for the number of pounds of salt ₁ (t), ₂(t), and z3(t) at time t in tanks A, B, and C, respectively. Write the model in matrix form and then solve it using eigenvalue/eigenvector techniques assuming that 21 (0) = 15, 22(0) = 10, and 23 (0) = 5. Will all of the tanks eventually be free of salt? Use your solution to justify your answer. pure water 4 gal/min 200 gal mixture 4 gal/min 150 gal mixture 4 gal/min امع 1000 mixture 4 gal/min

Accurately sketch the spectrum (magnitude only) of the following function y(t)=x(t) \cos (2 \pi 10 t) \text { if } x(t)=3 \operatorname{rect}\left(\frac{t}{2}\right)

4. Determine which of the following systems is linear or non-linear. Show proof a. y(t) = 2x(t) – 5 b.·dy/dt + 4y(t) = 2x(t) C.dy/dt+2ty(t) = x(t) d.dy/dt+ 4y(t) + 1 = x(t) e.(dy/dt) + y(t) = x²(t) f. (dy/dt)² + y(t) = x(t)

For t E[1,5], the upward velocity of a rocket is given by a quadratic expression v(t)=at2+bt+c. The upward velocity of the rocket is recorded

A vibrating system is described by the equation (units are in Newtons): 5x + 125x = 10 cos 5t Compute the response of the system if the system is initially at rest.

Consider the circuit shown below. Find using circuit analysis techniques, Vab, the voltage across the terminals a and b, PRL, the power dissipated by the load resistor, RL, The power delivered to the load resistor by the voltage source, V1, and The The venin equivalent circuit presented to the load resistor, RL. Validate all of your answers with Multisim circuit analysis. Submit both sowing they produce the same result.

3. Consider the system tx' = [22]x, t> 0 with initial condition X(2) = [−12]. A Assuming solutions of the form x = where X, V are an eigenvalue/eigenvector pair of the given matrix, use techniques similar to those used to construct solutions to the constant coefficient linear homogeneous systems to solve the given initial value problem. Write your answer as a single vector.