knowing that x should be such so that its second derivative isthe same as the or

Question

knowing that x should be such so that its second derivative isthe same as the original function with a negative sign andmultiplied by a constant. How can it be proved that the secondderivative of x with respect to time is equal to the negativeangular frequency squared multipled by x, if x is equal to theamplitude times the cosine of (the angular frequence times timeplus the phase constant)? In other words how does x'' = - 2 x knowingthat x = A cos ( t + ) ? knowing that x should be such so that its second derivative isthe same as the original function with a negative sign andmultiplied by a constant. How can it be proved that the secondderivative of x with respect to time is equal to the negativeangular frequency squared multipled by x, if x is equal to theamplitude times the cosine of (the angular frequence times timeplus the phase constant)? In other words how does x'' = - 2 x knowingthat x = A cos ( t + ) ?

Explanation / Answer

all you need to do is to take two derivatives of the equation forx and then identify in the last equation the part of the answer thatis equal to the original x d/dx(Acos(wt+)) = A * (-w) sin(wt+) d/dx(-wAsin(wt+) =A*(-w)*w*cos(wt+)=-w^2*A*cos(wt+)=-w^2*x

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