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Express sin(5theta) in terms of sin(theta) and powers of sin(theta) only.

Consider the expression (cos(theta) + i*sin(theta))⁵. (Where theta a real parameter).By De Moirve's theorem, we know this expression is equivalent to cos(5theta) + i sin(5theta).We can also ap...

Answered by Peter F. • Further Mathematics tutor

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A mass m=1kg, initially at rest and with x=10mm, is connected to a damper with stiffness k=24N/mm and damping constant c=0.2Ns/mm. Given that the differential equation of the system is given by d^2x/dt^2+(dx/dt *c/m)+kx/m=0, find the particular solution.

The system is described by a homogeneous, second order differential equation d²x/dt²+(dx/dt * c/m) + kx/m =0. First, substitute the known constants (m,k,c) to get d²x/dt<...

Answered by Christodoulos K. • Further Mathematics tutor

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Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)

The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -...

Answered by Joshua P. • Further Mathematics tutor

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