Find the motion of the mass-spring system modeled by the ODE and initial conditions. y" +26y' +168y = 1632 sin(12t), y(0) = -1.2, y'(0) = -59.2 y(t) =

Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that Force (F) = 640 Newtons Distance (x) =4 meters Mass (m) = 40 kilograms Upward velocity…

Q: The motion of a mass on a spring is described by 3y" + 4y = 0, y(0) = 5, y'(0) = 6. What is the…

A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: (b)y" = 2y(y'), y(0) = v2, y'(0) = -1 %3D %3D

A:

Q: H. JJ HY BY 4.6 where y(0)=0 y'co)=2

A: Given differential equation is y''+4y'+3y=4e-x with y(0)=0 and y'(0)=2We know the formula that PI of…

Q: y" - Y+1 = cos(+) u(

A:

Q: 1 y" + (у)? %3D уу' у(0) %3D 1, у'(0) -

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Q: y"+ 4y' + 8y = 30e−x/2 cos 5x/2

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Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: y" y'' +(cos xc)y' + ну =0

A: As per the question we are given the following second order homogeneous differential equation : y''…

Q: cos² xy' = (1 + y²)

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Q: Solve Y" - 6y + 13y = cos(4x)

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Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: A 1 kilogram mass is attached to a spring hanging vertically from a ceiling. At time t = 0, the mass…

A: (a) Here m=1,  k=1y(t) is the position of the object below the equilibrium position. Downward…

Q: 1 Find h' (u). Show your work. Let h(u) = 4u³ – - u?

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Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that a force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to…

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

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Q: A mass that weighs 8 pounds stretches a spring 6 inches. The system is acted on by an external force…

A:

Q: Nitin

A: (a) y(t)= ±5.83 cos(3t-30.96o)(b) Time period of the motion = 2.09 s      Frequency of the motion =…

Q: Solve: y(1) Given: y'-y=1, y(0)=0

A: