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The ODE mx'' + cx' + kx = 0 is used to model a damped mass-spring system, where m is the mass, c is the damping constant and k is the spring constant. Describe and explain the behaviour of the system for the cases: (a) c^2>4mk; (b) c^2=4mk; (c) c^2<4mk.

In the case c²>4mk, the characteristic equation has two distinct real roots; this represents overdamping. The system does not oscillate, and x approaches zero as time approaches infinity.In ...

Answered by Oliver G. • Further Mathematics tutor

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How do I determine whether a system of 3 linear equations is consistent or not?

First, form the system into a 3x3 matrix using the coefficients. Find the determinant of this matrix.If the determinant =/= 0, then the matrix is singular and has a unique solution. The system is consiste...

Answered by • Further Mathematics tutor

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What sort of mechanism is used during monobromination of benzene?

Electrophilic Substitution

Answered by • Chemistry tutor

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Explain the difference between the light dependent and light independent reactions of photosynthesis (2 marks).

Light dependent reactions occurs in the thylakoid membrane whereas light independent occurs in the stroma of the chloroplastLight dependent reactions produces the substrates for making ATP whereas ATP is ...

Answered by • Biology tutor

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What is the gradient and the y-intercept of the graph y = 3x + 7 ?

Based on the straight line equation of y = mx + c, where m is the gradient and c is the y-intercept, 3 would be the gradient and 7 would be the y-intercept.

Answered by Cyro B. • Maths tutor

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