A particle moves in SHM with centre O and passes through O with speed 10sqrt(3) cm/s. by integrating acceleration = - n^2 * x, calculate the speed when the particle is halfway between its mean position and a point of instantaneous rest.

\(\displaystyle a = -n^2*x\)

\(\displaystyle \frac{dv}{dt} = -n^2*x\)

\(\displaystyle \frac{dv}{dx}*\frac{dx}{dt} = -n^2*x\)

\(\displaystyle v*\frac{dv}{dx} = -n^2*x\)

\(\displaystyle \int{vdv} = -n^2\int{xdx}\)

Now find the integration. To find the constant of integration, put v = 0 when x = A, the amplitude.