Consider the spring-mass-damper system (SMD) mounted on a massless cart as shown in Figure 1. The mathematical model of the system is given by: d'y dy m ·+b+ky=b+kxx dt² dt Where m is the mass of the cart, x = u (input of the system), b is damping coefficient, and k is spring constant. If m=1 kg, b=2 N-s/m, and k=10 N/m. Answer the following questions: Mascos cart dx 111 dt Figure 1: SMD on massless cart (2-a) If x(t) equals zero, solve the differential equation (ie, find the general solution of the resulted homogeneous differential equation).

Q: X Z=1 R N -x=ln4 x = ln (t + 2), (e) Find the area of R. Consider a structure D with a curved solar…

A: The diagram of the structure is given by  The region R is bounded by the curves x=ln2, x=ln4, y=0…

Q: The position of an object attached to a spring is given by s (t) = cos(4t) - sin(4t), where t is…

A:

Q: Find the order of the matrix.           10 –19 19 16 21 –18 –4 0

A: The given matrix is as follows: 10-19191621-18-40 There are two rows and four columns in the above…

Q: Using composite trapezoidal rule evaluate the integral ∫0.5 0 f(x)dx

A:

Q: Find all local extrema for the function f(x,y)=-4x +y +32x²-8y² +1 and then match the equation with…

A:

Q: Question 20 Let V be a vector space and suppose T: V→ V is a linear map satisfying T2 = T. Prove…

A:

Q: a) Determine if the table represents a linear, quadratic, or exponential function. b) Use Desmos.com…

A: (1)      Since the first difference is same and the second difference are all equal to zero So, the…

Q: Find the average value of  f on the given interval.(b) Find c such that  fave  =f(c).(c) Sketch the…

A: Given: fx=x-32, 2, 5. To do: (a) Find the average value of f on the given interval. (b) Find c such…

Q: 2 x+16x³+9x+256x+256=0 4 3 Find the values of x?

A:

Q: Surface integrals using a parametric description Evaluate the surface integral ∫∫S ƒ dS using a…

A: Given: fx, y, z=x2+y2; S:x2+y2+z2=36, z≥0To find: ∬sfx, y, z dS using a parametric description of…

Q: i) a horizontal plane, (ii) the plane consisting of points satisfying the condition that x = 0 (aka…

A: As your Que has more than 3 subparts we shall solve first three subparts only. For others kindly…

Q: c) For a periodic function y(t) with period T, its Fourier series may be represented in complex form…

A:

Q: Two oscillating sinusoidal voltage signals v₁ and v₂ of amplitude 2 V and 1 V, respectively, at a…

A:

Q: maxx,y {f (x, y) = x+y: 2x + 4y = 8}

A:

Q: Find the values of a, b, c, and d in the matrix equation below. [19]+[77]-[143] a || b = C = d = a b…

A:

Q: Find the limit (enter 'DNE' if the limit does not exist) 1) Along the x-axis: 2) Along the y-axis:…

A:

Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 3x…

A: Given that the linear programming problem Maximize  z=3x-7ysubject to  y≤x ⇒x-y≥0…

Q: Find the Laplace transform of the given function: t 2 f(t) = L{f(t)} = (0, t²4t+8, s>0

A:

Q: A system of coupled ODEs, where x = x(t), are expressed in the matrix form X x' = (-10³4)x where x =…

A: x'=73-10-4xx0=-7-8

Q: Determine the types of base functions used to create each of the following graphs. N 1 1 1 1 S N - 4…

A: Given: Three graphs are given. To do: We need to determine the type of base functions used to create…

Q: (Find the value of the solution at x = 1 of the following initial value problem.) (23 (x³ + 1) +9x²y…

A:

Q: Solve the equations, giving your answers in exact logarithmic form each time (a) sinh x = =coshx;…

A: We solve the following equations.

Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 6x…

A: The given linear programming problem. maximize Z=6x+y Subject to the constraints, x-y≤03x-y≥0x,y≥0…

Q: 4. Find the general solution of y"(x) + y'(x) + y(x) = 0

A: y''x+y'x+yx=0

Q: 2. Let ECR and let x E R. We say that is detached from E if there exists 8>0 such that (x8, x+8) n E…

A:

Q: Consider the equation of a tractrix (a) Find dy/dx. (b) Let L be the tangent line to the tractrix at…

A: Given: Equation of a tractrix is y=asech-1xa-a2-x2 ,a>0. To Find : a) dydx b) When L intersect…

Q: Find the partial derivatives indicated. Assume the variables are restricted to a domain on which the…

A:

Q: (b) Give a qualitative explanation for why the sequence gn(x) = xn is not equicontinuous on [0, 1].…

A: Given: gnx=xn. To Explain: Why the sequence gnx=xn is not equicontinuous on [0, 1]. Also, check…

Q: a) A curve y = f(x) > 0, a ≤ x ≤ b is rotated around the x axis. Derive, with the aid of a suitable…

A:

Q: 1. Write TRUE if the statement is always correct. Otherwise, write FALSE. 1. The set S = {(2, 8, 5),…

A: Answer follows

Q: Answer the q

A: Question 3:  Given the triangle with vertices (2,6), (1,-2), and (-3,-2). part A to graph the…

Q: The equation of line s is y=(5)/(7)x+8. Line t is parallel to line s   Solve asap in 2 min pls i…

A:

Q: Let B and F be the following matrices.       [ -9  -7  -3  -3 ] B=  [ 7  10  8  -8 ]       [ 6   5…

A: Given matrices are B=-9-7-3-37108-865-36  and  F=-1410-5-2-70-10907-5.   Find the matrix B+F.

Q: 1. Consider the Surface S₁ with equation x² – 4 = 2z • Draw and sketch the graph of S₁ in R³.…

A: The surface S1 with equation x2-4=2z. To draw the surface S1 in ℝ3.

Q: TU TT 1. Use Taylor Series Expansion to approximate the value of f(x) = sin(x) at xi+1 = and x₁ ==…

A: Given f(x)=sinx n f n(x) f(π4) error π3-π4=π12 0 sinx 0.707 π12 1 cosx 0.707 π12 2 -sinx…

Q: Given: f(x) = (x²,0 < x < 1) (π, -1 ≤ x < 0) a) Find the FOURIER SERIES of the given STEP FUNCTION.…

A: Given function is: fx=π,        -1≤x≤0x2,           0≤x≤1 (a) The fourier series is:…

Q: Let f(x) be a generating function for the sequence (an)nzo. Find the generating function g(x) for…

A: The generating function for the sequence ann≥0 is given fx and the generating function for bnn≥0 is…

Q: a. Suppose that f(x) is differentiable for all x in [0, 1] and that f(0) = 0. Define sequence {a,}…

A: Suppose f(x) is a differentiable function and a sequence is defined as an=nf1/n. (a) To Show:…

Q: Formulate a linear programming problem that can be used to solve the following question. A firm has…

A: Since we have given that a firm has plants in Boston and Baltimore that manufacture three models of…

Q: For the function f(x,y) = 5x² + 6y2, find the following. a. b. f(x+h,y)-f(x,y) h f(x,y+h)-f(x,y) h…

A: The given function fx, y=5x2+6y2. We have to find the following values, a) fx+h, y-fx, yh b) fx,…

Q: Write the cubic polynomial function f(x)in expanded form with zeros −6,−4, and 1,,given that…

A:

Q: Let be unknown constants and consider the linear system: Nu₂ 10 X 2 x -7x + + 5 y 9 y + 33 y + 4 z =…

A:

Q: 4. (i) Let V be a real inner product space, with the inner product denoted by (,) and the associated…

A:

Q: 3. Use False-Position method to solve the same problem in Number 2. Use the same lower and upper…

A: As per the instruction we will only solve the question 3. The false position method is a…

Q: Refer to the graph to answer each of the following questions. For part (a), use interval notation to…

A: (a)  graph is concave down in interval = (3, 5) U (7, 8)

Q: 2. Farmer Conor wants to build a rectangular pen for his pack of Llama's. He has a gorge with a…

A: The total fencing available is 274 feet. The rectangular pen has the river on one side which need no…

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

Q: Find the inverse Laplace transform -{F'(s)} of the given function. 8s² 14s + 196 s(s²+49) Your…

A:

Q: Q3. Consider the following optimal control problem. min [~ ² {p(x(t))² + (1 - 4) (u(t))²} dt s.t.…

A: As per the question we are given an constrained optimal control problem where the system is modelled…

Q: Find the particular solution of the given ODE (y-. + y²) dx - xdy = 0 when x = √3, y = 1

A: