Consider a following model of an oscillator and solve in Sim

Consider a following model of an oscillator and solve in Simulink: For x(o) = 0, x\'(0) = 0, x\"(0) = 0 dx3/dt3 = 20 tan(1.5t) + 6 dx2/dt2 - 1.5 dx/dt + 6x Simulink model Simulink solution with output plot Re-solve the problem in Matlab and compare the results (show both graphs)

Solution

uation 1

$$\\dot{m}_{ai} = f(\\theta)\\cdot g(P_m) = \\mbox{mass flow rate into manifold (g/s)}$$

$$f(\\theta) = 2.824 - 0.052361\\cdot\\theta + 0.10299\\cdot\\theta^2 - 0.00063\\cdot\\theta^3$$

$$g(P_m) = 1; \\mbox{ if } P_m \\le P_{amb}/2 $$

$$g(P_m) = \\frac{2}{P_{amb}} \\sqrt{P_mP_{amb} - P^2_m}; \\mbox{ if } P_{amb}/2 \\le P_m \\le P_{amb} $$

$$g(P_m) = -\\frac{2}{P_m} \\sqrt{P_m P_{amb} - P^2_{amb}}; \\mbox{ if } P_{amb} \\le P_m \\le 2P_{amb} $$

$$g(P_m) = -1; \\mbox{ if } P_m \\ge 2P_{amb} $$

$$\\dot{m}_{ai} \ ightarrow \\mbox{mass flow rate into manifold (g/s); } $$

$$ \\theta \ ightarrow \\mbox{throttle angle (deg);}$$

$$ P_m \ ightarrow \\mbox{manifold pressure (bar); } $$

$$P_{amb} \ ightarrow \\mbox{ambient (atmospheric) pressure (bar);}$$