The system y(t)=x(t)cos[2(pi)t] is O nonlinear time invariant nonlinear time variant O linear time variant linear time invariant
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Q: The system y(t)=x(t)cos[2(pi)t] is linear time invariant O nonlinear time invariant O linear time…
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Please help, I need a solution for this LTI System problem. Please answer in 20 minutes.
![The system y(t)=x(t)cos[2(pi)t] is
O nonlinear time invariant
nonlinear time variant
O linear time variant
O linear time invariant](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099318eb-d94e-4371-9177-5fd1fd819e1d%2F5f0bb2b6-c254-4edd-9b27-1c21fd0f9e4c%2Fme6fp1_processed.png&w=3840&q=75)
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- A block spring system oscillates in a simple harmonic motion on africtionless horizontal table, its displacement varie with times according to x(t)=0,2cos(2t_3.14/4) the earliest time the particle reaches position x=0,1m isA velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
- The response of a certain dynamic system is given by: x(t)=0.003 cos(30t) +0.004 sin(30r) m (5Mks) Determino: (i) the amplitude of motion. (2Mks) (ii) the period of motion. (in) the linear frequency in Hz. (4) the angular frequency in rad/s. (2Mks) (2Mks) (2Mks) (2Mks) (v) the frequency in cpm. (vi) the phase angle. (2Mks) (vii) the response of the system in the form of x(t) = X sin(t +$) m.I need a Signal-Flow Graph for the element in the image below. Please solve with images and details. Thanks!Obtain the steady-state difference (f(∞) - v(∞) between the input and output of the following model: Tv + v= bf(t), where b is a constant and f(t) = mt. Assume that v(0) = 0 and that the model is stable (T > 0).
- Sketch the level response for a bathtub with cross-sectional area of 8 ft 2 as a function of time for the following sequence of events; assume an initial level of 0.5 ft with the drain open. The inflow and outflow are initially equal to2ft3/min.(a)The drain is suddenly closed, and the inflow remains con-stant for 3 min (0≤t≤3).(b)The drain is opened for 15 min; assume a time constant in a linear transfer function of 3 min, so a steady state is essentially reached (3≤t≤18) (c)The inflow rate is doubled for 6 min (18≤t≤24).(d)The inflow rate is returned to its original value for 16 min(24≤t≤40).A certain mass is driven by base excitation through a spring (Figure P4.13). Its parameter values are m = 100 kg, c = 1000 N * s/m, and k = 10,000 N/m. Determine its peak frequency w_p, it’s peak M_p, and its bandwidth.a)If the system has a transfer function of the form G_P (s)=H(s)/(V_m (s) )=μ/(1+Ts) where µ is the gain and T is the time constant, calculate values for µ and T for the case where the valve is at position 3. Hints: Use the constants and information in table 1. The dynamics of the water tank can be found by applying the continuity equation: qin - qout = rate of change in water tank
- In this Problem, the system of Fig. 5.4.14 (Attached) is taken as a model for an undamped car with the given parameters in fps units. (a) Find the two natural frequencies of oscillation (in hertz). (b) Assume that this car is driven along a sinusoidal washboard surface with a wavelength of 40 ft. Find thetwo critical speeds. m = 100, I =1000, L1 =6, L2 = 4, k1 = k2 = 2000Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0The response of a system is given by xt=0.003cos 30t +0.004sin 30t m. Determine (a) the amplitude of motion, (b) the period of motion, (c) the frequency in Hz, (d) the frequency in rad/s, (e) the frequency in rpm, (f) the phase angle, and (g) the response in the form of xt=Asin (ωt+φ)