Consider a system whose model is given by dx(t)/dt + 0.4 x(t) = sin(3t). What is the time constant of this system? Do not include units. Write your answer in scientific notation with 3 significant figures (2.14e0).

(b) An object is vibrating with simple harmonic motion (SHM), x(t) = A sinøt of amplitude, A = 15 cm and frequency, f=2 Hz. [Sebuah objek yang bergetar dengan gerakan harmonik mudah, x(t) = A sinot yang amplitud A = 15 cm dan frekuensi, f = 2 Hz.] (i) Determine maximum acceleration and maximum velocity of the vibrating object. [Tentukan pecutan maksimum and halaju maksimum untuk objek bergetar tersebut.] (ii) Calculate the acceleration and velocity for the displacement vibrating object, x(1) = 12 cm. [Kirakan pecutan dan halaju bagi sesaran objek bergetar, x(t) = 12 cm.]

Using a value of k/m = 270, write state-space equations for the undamped two-story building system. Using that result fill in blanks to identify A, B, C and D matrices. [A] = 0 0 [B] = 0 0 [C] = 1 [D] = |0 1 10 0 0 0 0 10 -270 0 0 1 0 0 0

A projectile is launched with a velocity of 100 m/s at an angle of 30° above the horizontal. Create a Simulink model to solve the projectile's equations of motion, where x and y are the horizontal and vertical displacements of the projectile. X=0 x(0) = 100 cos 30º x(0)=0 ÿ=-g y(0)=0 y(0)=100 sin 30º Use the model to plot the projectile's trajectory y versus x for 0≤t≤10 s.

4. For the fluid system in Fig 6 construct the linear graph, identify the state variables, and derive the state equations. The output variables are the pressure p₁ and på at the tanks. C₁ Aut I,R 0,01) - Figure 6: An fluid system R₂ V (t) ww Rs ERL L V (1) Figure 7: A tuning circuit for radio

hey can i get help with these two questions please. thank you.

A single degree-of-freedom linear elastic structure was subjected to a series of harmonic excitations, one at a time. The excitations had the same forcing magnitude but different forcing frequency. Forcing frequencies and observed peak steady-state displacements are shown in the graph below. Find the natural period and damping ratio of the structure. Displacement (mm) 60 50 40 30 20 10 0 0 1 2 . 3 4 Forcing frequency, f [Hz] 5 4. 6 7