4. Find the steady state periodic solution, Xsp(t) of the following differential equation. x" + 5x...
(1 point) Math 216 Homework webHW7, Problem 10 Find the steady periodic solution to the differential equation x" + 3x' + 25x = 4 sin(3t) in the form Xsp(t) = C cos(wt – a), with C > 0 and 0 < a < 21. Xsp(t) = 4/sqrt(337) cos
please answer both questions
3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series of f. f() = 6(1-1),0 <t< 4. Find the steady state periodic solution, *xp(t) of the following differential equation. *" + 5x = F(t), where FC) is the function of period 2nt such that F(t) = 18 if 0 << < 1 and F(t) = -18 if t <t <200.
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
2. Assume steady-state conditions exist at 0. (a) Find the differential equation for it(t) for t> 0 for the circuit below (b) Find the form of the solution (c) Find the initial conditions (d) Evaluate the coefficients for the solution. 4A 7 A 3. Find the voltage across the capacitor as a function of time. 30Ω 4u(t) A + 5A 3 H 27
1) Write a differential equation describing this system. This means find the equation of the line in the graph. df ar= 1x-80 2) Find the general solution to this differential equation. Find the function f(x) whose derivative is the equation of the line graphed. The solution is: f(r) -.5x 2-80x 3) Now given that function f(x) includes the point (0, 100) find the exact solution of the differential equation found in 1). In addition to general solution you will have...
The dynamics of a spring-damper-mass system is defined by the following differential equation, č + 4€ + 5x = f(t),x(0) = 1, *(0) = 2, where f(t) is a step input with magnitude of 10, i.e. f(t)=10-1(t). Find the solution x(t) of the differential equation using Laplace transformation method.
What is the steady state output, x s(t), for the following system? x + 5x = 6sin8t x(0) = 0
Find the general solution of the following differential equation. Primes denoto derivatives with respect to x. x(5x + y + y(15x + y) = 0 The general solution is (Type an implicit general solution in the form F(x,y)=C, where is an arbitrary constant. Do not explicitly include arguments of functions in your answer)
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'(0)=x(0)=0 Find the solution of this differential equation using Laplace transforms. F(t) 7m
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1...