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Question: A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3 pi/5)seconds and the amplitude is 0.4 metres. Calculate the maximum speed of the particle. Anwer:...

Any odd integer can be represented by 2m+1 for some integer m (can prove that 2m+1 is always an odd number if needed). (2m+1) 2 =4m 2 +2m+2m+1=4m 2 +4m+1=4m(m+1)+1 simple factorisation. m and (m+1) are conse...

First assess that the initial case of where n = 1 is true. In this case, 6+9=15=5 3, so we can see that the case is true.We can then assume that 6 k +9 is a multiple of 5, so we can let 6 k +9 = 5A for some ...

4sinx(cosx)^3 - 4cosx(sinx)^3

First we need to find the complementary function - the solutions of y'' -3y' + 2y = 0. By setting y=Ae^(kx) (A is a constant) we get :A(k^2 - 3k + 2)y = 0. This means k^2 - 3k + 2 = 0 =(k-1)(k-2). If 2 thing...