The cart in the figure below weighs 64 pounds and is attached to the wall by a spring with spring constant k = 32 lb/ft. The cart is pulled 3 inches in the direction away from the wall and released with no initial velocity. Simultaneously a periodic external force Fe = f (t) = 16 cos 4t is applied to the cart. Assuming that there is no air resistance, find the position x = x(t) of the cart at time t. Note particularly that |x(t)| has arbitrarily large values as t → o, a phenomenon known as pure resonance and caused by the fact that the forcing function has the same period as the free vibrations of the unforced system. M о

Q: Show that the dictionary order topology on the set R x R is the same as the product topology Rd × R,…

A:

Q: Solve by theorems of linearity and translation. f(t) = cos t + sin t

A:

Q: Sx² sin 2x dx

A:

Q: Jump to Problem: 1 2 Problem 1. (3 points) How many shortest lattice paths start at (5, 5) and a.…

A:

Q: Show that the dictionary order topology on the set R x R is the same as the product topology Rd × R,…

A:

Q: Find the maximum and minimum values of the function f(x, y, z) = x²y² z? subject to the constraint…

A: For the solution of the problem follow the next steps.

Q: Verify that lxl:|Ž Ž1% P) is normed spase: and show that nokmed Spase Spase:

A:

Q: Q1: Use differentials 3x-2 the appsorimate ay to AY from clanges when and x 2 to 2:63-

A: Given function is y=3x−2. We have to approximate ∇y when y=3x−2 and x changes from 2 to 2.03.…

Q: Show that the dictionary order topology on the set R × R is the same as the product topology Rd × R,…

A: A basis for the product topology on ℝd×ℝ is B=x×(y1,y2)|x,y1,y2∈ℝ, y1<y2 These are just products…

Q: Students at Blake's high school must have a B average in order to participate in sports. Blake has a…

A:

Q: Can someone help me to approximate this double summation into an expression that contains a and b?…

A: The value of ab=0.625

Q: 2. (3+j4)(6+)7) convert to polar form (Az0) Hint: x = en(x)

A:

Q: Use the two properties L1 and L2 to show that the following are linear transformations. (d) T:R' →R'…

A:

Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

A:

Q: Find the general solution of each differential equation, and when initial conditions are given, the…

A:

Q: The z-transform of x(n) is X(z) = 1 + 2z1, Iz/ # 0. Find the z-transform of the sequence x1(n) = x(3…

A: Given, x(n)→X(z)  (z-transform)X(z)=1+2z-1 To find: z-transform of x1(n)=x(3-n) + x(n-3)

Q: 3. Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

A: We have to find orthogonal trajectory for the family of straight lines passing through 3,-5

Q: Evaluate L{t cosh 4t. 1 1 + (s – 1)’' (s+1)* А. В. (s-1)* (s+1)* 1 1 С. (s –4)° (s+4)' 3. D. (s-4)*…

A:

Q: For some of the most interesting laws of modular arithmetic (Choose some of your liking, but do…

A: This is a problem of mudular arithmatic.

Q: 1. (3x'+ 2y')dx + 2xydy=0

A:

Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: 8. Find the equation of the line tangent to the graph of y tan (sin) when z= V2/2.

A:

Q: Use the following matrices for the next 3 questions 1 2 0| B= 3 4 5 0 0 6 1 5 1 4 -1 2 1 1 1 C= 1 1…

A:

Q: a) Find the degree 2 Taylor polynomial T2 (x) for the function f (x) = 4xe centered at the point a…

A:

Q: Let L : R → R² be defined by L(æ) = L T2 (:) - () Show that L is not a linear transformation by…

A: We have to prove that L is not a linear transformation.

Q: The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base…

A:

Q: Use the Gram-Schmidt process to find an orthogonal basis for the column space of the following…

A: Given: Let us consider the given matrices, a) -2-6-14-16-18-210215-20-16

Q: For a, b, c, d e R, show the following. (a) If a >b and c> d, then a +c>b+d.

A:

Q: All primates are curious. Some primates are carnivores. Thus, some carnivores are curious. * 1 point…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: Consider the following graph: a) Find a maximum set of pairwise internally-disjoint uv- paths. b)…

A:

Q: 1. Determine the graph of the given equation. a. x2 + y? + z2 – 8x + 4y + 2z– 4 = 0 b. x2 + y2 + z2…

A:

Q: What is the z transform of x(n) = 1, 0<n< 5 a. z1 + z2 + z3 + z4 + z-5 b. z + 1 + z1 + z-2 + z-3 +…

A: Here first we find Z transform of unit step function, then find Z transform for 0≤n≤5

Q: (a) Find the crcal numbers of f. (Enter your answers as a comma separated fist.) an answer des not…

A:

Q: Determine whether the follwoing inferences are valid (translate them into symbolic form then…

A: We have to determine that the given inferences are valid or not.

Q: Let n 2 2. Assume that Fn is prime. show that -1.

A:

Q: Convert the following integers into ordinary decimal representations. (а) 0b1111 15 (b) 0о17 15 (с)…

A:

Q: 3. x'sec'ydy – (1– 2x²tany)dx = 0 4. dy – (x - y + 1)°dx = 0

A:

Q: -21 e * u(t) + e ª u(1)

A: The given function is    e-tut+e-2tut Let xt=e-tut and x1t= e-2tut

Q: Use the method of false position to find the fourth root of 32 correct to three decimal places

A:

Q: Question 5 Find the solution. dy y dx x A B y = y = 9. D) y = -|00

A:

Q: If z/w = 6 - j8 when z = 22 + j4, what is the argument of w?

A: To find The argument of w.

Q: Show that the function f (x) = 1/x2 is uniformly continuous on the set [1, ∞) but not on the set (0,…

A: Solution

Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

A:

Q: Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R. a = 2 b…

A:

Q: 4.43. xe" dx + (y-1)dy 0; y(0)=0

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: (1) Consider the Gaussian kernel of the form 1 p(x,t) = V2nt Show that p(x, 0+) = 8(x). Remark 0.1.…

A: First the standard definition of the Dirac delta function is defined. Then, limit of the Gaussian…

Q: Bernoulli Equation (11) (x²y* – 1)ax + x³y³dy = 0 (12) x2 + 2xy dx

A:

Q: Solve the following ODE. 3y(x) +4y(x)– 4y"(x) = 8 ,(3)

A: As per Bartleby policy we can only answer one question  Hope you understand

Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

A:

Q: 4. Show that V2 ¢ Q(v3) and Q(V2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

A: We know that ,  ℚ2 = a + b2  / a , b ∈ ℚ ℚ3 = a + b3  / a , b ∈ ℚ  We need to prove that , 2 ∉ ℚ3 On…