Find the resistance R so that the circuit is critically damped.

Q: b) Use Laplace transform to solve the system of differential equations UTM dr UTM x = 4y, dt y+Bet…

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Q: we considered the Position Servo described by the state equation where A = T x(t) = Ax(t) bu(t) + IT…

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Q: 4. Consider the RC circuit depicted in below with input x(t) and output y(t). a) Write a…

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Q: Consider the logistic equation in the form P'(t) = CP − P2. C = 4 Draw the directional field.…

A: Below given clear explanation

Q: 5. A 10kg mass is attached to a spring hanging from a ceiling. This causes the spring to stretch 2m…

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Q: For the following scenarios derive the required mathematical model in the form of a differential…

A: Given: a) The instantaneous current i at time t in a simple DC RL circuit. b) The displacement x of…

Q: uy constants. Show that lim,y(t) = 0 for every solution of this equation.

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Q: The equation that describes the accumulation of charge, denoted as q(t), on the capacitor within an…

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Q: Find r(t) that satisfies the initial condition(s) r″(t) = −4 cos tj − 3 sin tk,    r′(0) = 3k,…

A: Given r″(t) = −4 cos tj − 3 sin tk,    r′(0) = 3k,    r(0) = 4j

Q: Using the Laplace transform method, solve for t> 0 the following differential equation: d²x dx + 5a…

A: Given second order differential equation d2xdt2+αdxdt+βx=0 Solution of a differential equation…

Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: d³x + 2d²x - dx -2x=4+e²t dx+ 207 de dt³ dt² dt x(0)=1, x'(0)=0, x’’(0)= -1

A: The given initial value problem, d3xdt3+2d2xdt2-dxdt-2x=4+e2t with the initial conditions x0=1,…

Q: Solve the ODE (6xy-e¯y)dx + (3x² + e˜³) dy = 0 with the Initial Condition y(1) = 1 Then Create a…

A: Note: Since the value of y at x=1 is already given as initial condition, therefore it will be same…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.