A 1 kg mass is attached to a spring with a spring constant k = 9N/m. A periodic force F(t) = cos(wt) (in Newtons) was then applied to the mass. The figure below shows a graph describing the mass's motion, y(t), resulting from the application of the force: y 2 1 -1 -2 4 www 6 8 10 12 (a) Write down the initial value problem describing the mass's motion, (b) Determine the value w appearing in F(t) = cos(wt). t

Q: Within real numbers, let A = {z : 0 < x < 1} and B = {r: 0 < x < ∞o}. Define f: A → B by f(x) = 1…

A:

Q: x'= x +z, y'= x +y, z = 2x - z, x(0) = 1, y(0) = 0, z(0) = 0

A:

Q: Suppose that a 2 x 2 matrix A has an eigenvalue 2 with corresponding eigenvector [22] and an…

A: For eigen value  the eigen vector is  and for eigen value  the eigen vector is

Q: 1. Show that 2! 4! 6! (2n)! ≥ ((n + 1)!)" for ne z+. . ...

A: To prove the inequality  for n∈Z+, we can use mathematical induction.Base Case: Let's check the…

Q: Maria has a portfolio consisting of 7 shares of stock A (purchased for $70 per share) and 4 shares…

A:

Q: Which of the following subsets of P2 are subspaces of P₂? DA. {p(t) | Jop(t)dt = 0} B. {p(t) | p(0)…

A: Note: As you have posted multiple subparts of question but according to the guidelines I will answer…

Q: could you do this on a piece of paper so that its easier to understand?

A:

Q: min z = 3x + y s.t. y-0.5x ≥ 1 y + x ≥ 3 x≤ 3 y ≤ 4 x, y ≥0 (a) On the following page, use the…

A:

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A:

Q: 3. Consider the following function f(x, y) = 1²y + 2y² - 2xy +6. (a) Find all first and second order…

A:

Q: For the vector field (x³z², o, -x²z), evaluate the line integral on the clase curve made by a square…

A:

Q: a) y n + 2] = 4y[n+ 1] + 5y[n] given that y[0]= 1, y[1] = 2.

A: Note: According to the guidelines we are allowed to solve one question at a time. Please post rest…

Q: 2. Use the root test to determine whether the series below converges or diverges. ∞ 2n Σ(1+2n²)n n=1

A:

Q: Give examples of functions f and g such that f and g do not have limits at a point c, but such that…

A:

Q: (b) Construct the full table of values for h. (Make sure to use the 'preferred' names for classes in…

A: Given h: is defined by h([a])=[3a-5]We have to find all values of h i.e, all elements of a of  and…

Q: Use the Laplace Transform to solve the initial value problem. Show all necessary work: y" + 2y' - 3y…

A: Consider initial value problem .Here intitial conditions are  and .To solve this problem using…

Q: Figuring a tip: You are having dinner at a burger restaurant. The price of your meal is $24.00 You…

A: You are having dinner at a burger restaurant. The price of your meal is $24.You are tipping 20%…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A:

Q: A dilation with center P and ratio r has equations x'= -2x + 3 and y2y4. Find P and r.

A: A dilation with center P and ratio r can be represented by the following…

Q: Suppose that a < b < c and f is continuous. Select the true statement. C с C [ 1 (2) de - [1(4) de +…

A: By using second fundamental theorem of calculus, we will find the property.

Q: Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = "…

A:

Q: Suppose x = a, e are two solutions to the cubic equation x³ + px = q . Use Viete's approach to find…

A:

Q: Set up the integral to find the volume of a right cone (z= sqrt(x^2+y^2)) with height 10

A: We have to set up the integral to find the volume of a right cone  with height 10

Q: If a is a similarity of ratio r and A, B, and C are distinct non-collinear points, let A' = a (A),…

A: Given information: and  are non-collinear points. is a similarity ratio . and  are the non-collinear…

Q: Convert the given initial value problem into an initial value problem for a system in normal form.…

A:

Q: 5. Consider the system in state variable form x = AX + Bu y = Cx + Du with A = [ ] B = [¹₁] C = [1…

A: i) We have to Determine the transfer function T(s)ii) We have to Determine the system's…

Q: actice Another X Use the inner product (u, v) = 2u1V₁ + U₂V₂ in R2 and the Gram-Schmidt…

A:

Q: Find general solutions for the following differential equations (a) x²y" - xy + y = 2xlnx + 10

A:

Q: Let de N. Assume that x, yez every n € N.

A:

Q: Use a calculator or program to compute the first 10 iterations of Newton's method when they are…

A:

Q: Given a knowledge base (KB) that consists of two components, A and B, one can check if a statement C…

A: is logically equivalent to Simplification rule: if  is true then  is true. Hypothetical syllogism:…

Q: j Recall that Mnxn (R) is the vector space of n x n matrices with real coef- ficients. Let A and B…

A:

Q: There is an equation that describes the cost function of Ridge, where j runs from 0 to p. So if p is…

A:

Q: Use a calculator or program to compute the first 10 iterations of Newton's method for the given…

A: According to the given data, find the 10 iterations using Newton's method:

Q: For , √3 tan $=1/153 T3 @= tan F6 xl P: IT 2 ^¹ (73) FAISzer 2²=3y² 2=√By Z= 7:mx ====√ √ 2 Y tan (3…

A: The region is bounded above by  and below by the cone

Q: Use spherical coordinates to find the volume of the region outside the cone = 1/4 and inside the…

A:

Q: Sc xe¹zdS, C is the line segment from (0,0,0) to (1, 2, 3)

A:

Q: A house sells for $165,000 and a 15% down payment is made. A mortgage was secured at 4.7% for 30…

A: To find the down payment, we start with the given information:House price: $165,000Down payment…

Q: Question (a) (b) We are given four data points: (c) Here is an uncompleted divided difference…

A: The divide difference table as shown below:

Q: Consider two fuzzy sets A and  B defined on the universe of discourse X={1,2,3,4,5} with the…

A: Fuzzy Union: The fuzzy union of two sets A and B is a set which contains all the elements of A and B…

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A:

Q: Detailed justifications are required! 6) Recall that Mnxn (R) is the vector space of n x n matrices…

A:

Q: Given that B=([1 -2 2].[1 -1 3). ([0-3-2]) is a basis of R³ and C= ([1-3 0], [0 1 0]. [-3 11 1]) is…

A:

Q: Solve the system below. IH + 5y -5x + 25y 25y -2x + +3w z + 19w = 10yz + 10w = The particular…

A:

Q: -1 2 Find an orthogonal basis for the column space of -1 2 -3 0 X 100 1

A:

Q: 1. Suppose V is the vector space of continuous functions f: [-1, 1] → R (a Show that (,): V × V → R…

A:

Q: The masses m, are located at the points P₁. Find the moments Mx and My and the center of mass of the…

A:

Q: The vector field F = e¯ª i — xe¯ªj is conservative. Find a scalar potential f and evaluate the line…

A:

Q: Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive.What is the…

A: The objective of this question is to find the probability that a randomly chosen integer between 1…

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A: Given that the function is