In order to determine the unbalance in a grinding wheel, rotating clockwise at \(2400 \mathrm{rpm}\), a vibration analyzer is used and an amplitude of \(0.1 \mathrm{~mm}\) and a phase angle of \(45^{\circ}\) are observed with the original unbalance. When a trial mass \(m=100 \mathrm{~g}\) is added at \(20^{\circ}\) clockwise from the phase mark, the amplitude becomes \(0.2 \mathrm{~mm}\) and the phase angle \(145^{\circ}\). If the phase angles are measured counterclockwise from the right-hand horizontal, calculate the magnitude and location of the necessary balancing weight.