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.
v^2/2 = - n^2*x^2/2 + C or
v^2 = -n^2*x^2 + K.
When x = 0, v = 10sqrt(3), v^2 = 300.
v^2 = -n^2*(x^2) + 300.
When x = A, the amplitude, v = 0. So
0 = -n^2A^2 + 300.
n^2*A^2 = 300.
Velocity at A/2 is given by
v^2 = -n^2*(A/2)^2 + 300
Substitute the value for n^2A^2 and find v.