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QUESTION 5...
A frictionless wire is bent into the shape of a cycloid curve, with coordinates given by...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
Please answer with all the steps, thank you! Question 1. (16 points] Solve each of the...
Please answer with all the steps, thank you!
Question 1. (16 points] Solve each of the following IVPs: (a) y" + 4y' + 4y = -32 cos(4x) + 3e-27, y(0) = -75, Y'(0) = - 128 (b) y'" – 4y" + y' + 6y = 10 sin x + 12e32, y(0) = 0, y'(0) = 1, y" (0) = 2 (c) y" – 24" = 16e2x – 36x + 14, y(0) = 6, y'(0) = 0, y" (0) = 2...
Engineering Analysis Homework #1 Problem #1 RLC Circuit: A simple electric circuit consisting of a resistor,...
Engineering Analysis Homework #1 Problem #1 RLC Circuit: A simple electric circuit consisting of a resistor, a capacitor, and an inductor is depicted. Switch Battery L = Capacitor Inductor Resistor The charge on the capacitor g(t) can be computed as a function of time and initial charge 4. q(t) = 4, cos () Where the decay rate B - 4 and frequency .= VE-(4) depend on the resistance R, the inductance L, and the capacitance C. Plot this function from...
please help me with as much as you could Calculus (4 marks) A firm estimates that the total revenue, SR(q), received from the sale of q goods is given by 5. R(x) = ln(1 + 1000 ) Calculate the mar...
please help me with as much as you could
Calculus (4 marks) A firm estimates that the total revenue, SR(q), received from the sale of q goods is given by 5. R(x) = ln(1 + 1000 ) Calculate the marginal revenue when q = 10. Explain what this result means. 6, (3 marks) Consider the function f(x) = x3 + 2. (a) Sketch a graph of y-f(x) on I-1,2 (b) Estimate the area bounded by y-f(x), the x-axis and the...
Z=61 Task 3: Answer the following: a. Evaluate: Siz cos(x) sin?(x) dx (10 Marks) b. The...
Z=61
Task 3: Answer the following: a. Evaluate: Siz cos(x) sin?(x) dx (10 Marks) b. The moment of inertia, I, of a rod of mass 'm' and length 4r is given by Ar (2mx? dx where 'x' is the distance from an axis of rotation. Find I. (5 Marks) 2r Task 4: Answer the following: Using the Trapezoidal rule, find the approximate the area bounded by the curve y = ze), the x-axis and coordinates x = 0, x =...
could you provide a detailed solution for this question. Like and comment are rewarded, thanks 2....
could you provide a detailed
solution for this question. Like and comment are rewarded,
thanks
2. Consider the system shown in the figure below. y m1 k,1 Mass mi moves horizontally along the x axis and its position is given by coordinate x1. It is attached to mass m2 by a light spring of spring constant k and natural length 1. The spring is constrained to oscillate in the r-y plane. Let the angle between the spring and the negative...
CAN YOU PLEASE ANSWER ALL THE QUESTIONS FOR ME I WILL GIVE YOUR ANSWER A LIKE...
CAN YOU PLEASE ANSWER ALL THE QUESTIONS FOR ME I WILL
GIVE YOUR ANSWER A LIKE
1. (8 points) Let r(0) = k tan o be a curve defined in polar coordinates, where k is a nonzero real constant. Find the correct formula for " dy dx 2. (10 points) Given below are the graphs of two functions y = f(x) and y = g(x). Use the graphs to find the indicated value. y = f(x) y = g(x) WN...
NOTE: PLEASE DO Q.3 Part d and e Answers are given below: Question 3 (16 marks)...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx...
Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for 1 (t) = - 16 - 7 ( g(t) = – 4 – 4t The Cartesian equation is y = Question Help: Message instructor Check Answer a. b. . 1 (t) = t cos(4) 1 vịt) = tsink) 1 (t) = 2 + cos(t) 18(t) = sin(t) = + + cos(t) (t) = + + sin(t) c. 9 d. 2 1...
By 5. (a) Verify that y = {24 sin x is a solution to the differential...
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
Please answer with all the steps, thank you!
Question 1. (16 points] Solve each of the following IVPs: (a) y" + 4y' + 4y = -32 cos(4x) + 3e-27, y(0) = -75, Y'(0) = - 128 (b) y'" – 4y" + y' + 6y = 10 sin x + 12e32, y(0) = 0, y'(0) = 1, y" (0) = 2 (c) y" – 24" = 16e2x – 36x + 14, y(0) = 6, y'(0) = 0, y" (0) = 2...
Engineering Analysis Homework #1 Problem #1 RLC Circuit: A simple electric circuit consisting of a resistor, a capacitor, and an inductor is depicted. Switch Battery L = Capacitor Inductor Resistor The charge on the capacitor g(t) can be computed as a function of time and initial charge 4. q(t) = 4, cos () Where the decay rate B - 4 and frequency .= VE-(4) depend on the resistance R, the inductance L, and the capacitance C. Plot this function from...
please help me with as much as you could
Calculus (4 marks) A firm estimates that the total revenue, SR(q), received from the sale of q goods is given by 5. R(x) = ln(1 + 1000 ) Calculate the marginal revenue when q = 10. Explain what this result means. 6, (3 marks) Consider the function f(x) = x3 + 2. (a) Sketch a graph of y-f(x) on I-1,2 (b) Estimate the area bounded by y-f(x), the x-axis and the...
Z=61
Task 3: Answer the following: a. Evaluate: Siz cos(x) sin?(x) dx (10 Marks) b. The moment of inertia, I, of a rod of mass 'm' and length 4r is given by Ar (2mx? dx where 'x' is the distance from an axis of rotation. Find I. (5 Marks) 2r Task 4: Answer the following: Using the Trapezoidal rule, find the approximate the area bounded by the curve y = ze), the x-axis and coordinates x = 0, x =...
could you provide a detailed
solution for this question. Like and comment are rewarded,
thanks
2. Consider the system shown in the figure below. y m1 k,1 Mass mi moves horizontally along the x axis and its position is given by coordinate x1. It is attached to mass m2 by a light spring of spring constant k and natural length 1. The spring is constrained to oscillate in the r-y plane. Let the angle between the spring and the negative...
CAN YOU PLEASE ANSWER ALL THE QUESTIONS FOR ME I WILL
GIVE YOUR ANSWER A LIKE
1. (8 points) Let r(0) = k tan o be a curve defined in polar coordinates, where k is a nonzero real constant. Find the correct formula for " dy dx 2. (10 points) Given below are the graphs of two functions y = f(x) and y = g(x). Use the graphs to find the indicated value. y = f(x) y = g(x) WN...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for 1 (t) = - 16 - 7 ( g(t) = – 4 – 4t The Cartesian equation is y = Question Help: Message instructor Check Answer a. b. . 1 (t) = t cos(4) 1 vịt) = tsink) 1 (t) = 2 + cos(t) 18(t) = sin(t) = + + cos(t) (t) = + + sin(t) c. 9 d. 2 1...
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
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