The motion of a damped harmonic oscillator is given by dx dt? +2 +2y = 0. dt (a) Change the equation to a two dimensional linear system. (b) Find and classify the fixed points in -0o
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- Please help solve the following systems but don't need to draw a phase portraitEx. 625. The sum of two numbers is 63 and their difference is 36. What are the two numbers (smaller, larger)? Use linear algebra techniques to solve the two simultaneous linear equations. Focus on the linear algebra technique. ans:2 Ex. 630. Refer to Fig. 630. Let n=84 Assign phase variables: x1=y and x2=x1dot. Determine the state variable equations. Answers: a11,a12,a21,a22,b1,b2,c1,c2,d ans:9A chemistry student heats a beaker that is at room temperature (30 ° C)by inserting it in an oven that has been preheated to 250 °C. If u is the temperature of the beaker in °C, what is the appropriate equation to model the temperature of the beaker. O du/dt = k(u –- 250) O du/dt = k(u – 30) O du/dt = k(250 – u) O du/dt = k(30 – u)
- Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? ✓ | 1. z ' = || a' ? 2. ': = ? 3.' = 4. a: = 11 8] -10 3 1 5 -2 1 -5 -13 10] -10 x2 A x2 с x1 (x2 B 2x2/ D Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.2023 5 Use the linear equation y(x-32), where x is the degrees Fahrenheit and y is the degrees Celsius, to convert each temperature. (a) 62 C to Fahrenheit (b) 7°F to Celsius (a) 62°C-F (Round to one decimal place as needed.) (0) 7°F-'C (Round to one decimal place as needed.). Question 18 of 20 >SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Consider a system of equations that represents a forced pendulum. a) Find the solution for the variables and graph the phase space. de dt dw dt = w, 1 sin(0) ∙W. (1)
- Solve the ifferential equation (D2-2D+2)y=cos9x= Find the general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. x' = -4 1 -6 XTwo children weighing 15 and 22 kilograms are sitting on opposite sides of a seesaw, both 2 meters from the axis of rotation. Where on the seesaw should a 10-kilogram child sit in order to achieve equilibrium?The 10-kilogram child should sit on the same side as the ? kilogram child, ? meter(s) from the axis of rotation.