What is the particular solution to the differential equation with the initial || dx condition y(e²) = –1?
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A: Option (b) is Correct.
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Q: Solve the initial value problem below using the method of Laplace transforms w"-12w'+36w=…
A: given; w"-12w'+36w= 180t+336, w(-2)=-1,w'(-2)=-5
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- Solve the initial value problem below using the method of Laplace transforms w"-12w'+36w= 180t+336, w(-2)=-1,w'(-2)=-5Suppose a spring with spring constant k=1 supports a mass of 1kg and is subject to a driving force f(t)=sin2t. The mass is initially at rest at its equilibrium point. At time t=2, the mass is hit with a sharp upward blow, so that the force of the blow is δ(t−2). Set up and solve (using Laplace transforms) an initial-value problem modelling this situation.NSLOM using Differential Equations
- A system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.Use the Dahamel integral method to derive expressions for the response of an undamped system subjected to the forcing functions shown in Figs. 4.46(a) to (c).find trasfer function Y(s)/R(s) if kc is 5 and plant is 1/(0.5s+1). input r(t) is a unit-step function
- laplace transformA cup of coffee with cooling constant k = 0.09 min- 1 is placed in aroom at temperature 20°C.(a) How fast is the coffee cooling (in degrees per minute) when its temperature is T = 80° C?(b) Use the Linear Approximation to estimate the change in temperatureover the next 6 s when T = 80°C.( c) If the coffee is served at 90°C, how long will it take to reach an optimaldrinking temperature of 65°C?Would you explain more about equations of motion and the Laplace transform in this question ?
- *Need answer only for the a3. Consider a mass spring system with an external force ?(?) = ?osin?o?. Let's assume ? is the mass of the object attached to the spring, ? is the spring constant, and ? is the damping coefficient. Let's also assume that ?(0) and ?′(0) are the location and speed of the object attached to the spring at time ? = 0. a) Find the general solution of the differential equation governing the motion of the spring, in terms of ?,?,?,?(0),?"(0),?0 and ?0. Your solution shall cover all possible cases including 1. the case with no damping and ?! is not equal to natural frequency of the system, ? =sqrt?/?. 2. the case with no damping and ?! is equal to natural frequency of the system, ? =sqrt?/?. 3. the three cases with damping (overdamped, critically damped, and underdamped).OBLEM 4. Using the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT: Use the periodic boundary conditions for the functions g(r) and s(x).Fill in the Blank Question: Simulations that have time derivative terms in their governing equations are considered to be _________ in nature?