Question

Model and plot in Simulink the differential equation of a given system: ?̈−4?̇∗sin(?)+√?(?)∗?−3?(?)=0
with the time-dependent external input signal ?(?)=sin⁡(2?)
Build a Simulink model to:
➔ Model the given differential equation.
➔ Plot x and ?̇ arranged in subplots with one above the other (see concept graphic below) in the same scope with ?̇ on top, including a legend naming each curve and axes labels.

Note:
• Use an appropriate source block to model the input signal y(t)
• You can use “a” instead of ?̈ and “v” instead of ?̇ for labelling in Simulink.
• Use “Ctrl + R” to rotate selected Simulink blocks.

Answer 1

Ÿ = ?ylt) - Fyx + 4 å sin(x) 2. Now take 4. 1. Generate signal ult) ( Ramp block, Sine ware block with external input) Pickup Xlt value from y, a take square not using sqrt block. multiply it with a It gives signal asy gain block with gain= 3 for signal Yet, It gines 3 y(+) Substract art (step 2) from it. It gives signal (3441-28) Using some fundo block, take sine of x (sm(xs), multiply it with åtv). It gives isina. Now use goin block of value 4 to 4 à son nesut of step 3 and 4. tuting Sumatto step 4. jne. (346+) –287) + 4 sind integrate result of steps twice to obtain, displacemenim sli = 5(3,497 XVG) dt) at obtain S. Now which ig equal to NOW 7.0. (+) 7 feed and values from v and a branets to scope block for plotting-

- Х untitled * File Edit View Display Diagram Simulation Analysis Code Tools Help 09 1.57 Normal untitled untitled oņa V 1 AN 3 + у Зу a V X Ramp Sine Wave Scope Gain Integrator Integrator 1 X.sqrt(y) V Gain 1 4 Product1 Х X IN Product sin(x) X Sine Wave 1 х u sqrt(y) Sart Ready 201% ode45

untitled File Edit View Display Diagram Simulation Analysis Code Tools Help 2 Normal untitled untitled Х Source Block Parameters: Ramp Ramp (mask) (link) Output a ramp signal starting at the specified time. Parameters AS Slope: 1 + Start time: * 0 Ramp Initial output: 0 Interpret vector parameters as 1-D 4 OK Cancel Help Apply X Product

=play Diagram Sind Function Block Parameters: Sine Wave X Sine Wave Output a sine wave: o(t) = Amp* Sin(Freq*t+Phase) + Bias Sine type determines the computational technique used. The parameters in the two types are related through: Samples per period = 2*pi / (Frequency * Sample time) Number of offset samples = Phase * Samples per period /(2*pi) Use the sample-based sine type if numerical problems due to running for large times (e.g. overflow in absolute time) occur. Parameters Sine Wave Sine type: Time based Ir Time (t): Use external signal Amplitude: h1 Bias: 0 Frequency (rad/sec): 2 Phase (rad): 0 OK Cancel Help Apply

lacus 7 Nama x Function Block Parameters: Sine Wavel parameters in the two types are related through: Samples per period = 2*pi / (Frequency * Sample time) Number of offset samples = Phase * Samples per period /(2*pi) Use the sample-based sine type if numerical problems due to running for large times (e.g. overflow in absolute time) occur. V Parameters 1 Sine type: Time based V S Time (t): Use external signal to Amplitude: Integrator 1 Bias: 0 Frequency (rad/sec): 2 Phase (rad): IN 0 Sine Wave 1 OK Cancel Help Apply

Scope HO RAKT 'Scope' parameters X General History Style Axes Number of axes: 2 | Floating Scope Time range: auto Legends Tick labels: bottom axis only Sampling Decimation 1 OK Cancel Help Apply 0 3.5 نيا

х - Scope AO DER OF 0 3.5 3 25 2 1.5 1 - 0.5 0 -0.5 0.2 0.4 0.6 0.8 1.2 1.4 1.6 Time offset: 0