In the desert there is a jail. After rebellion the single guard has been immobilized. He watched helplessly how prisoners left one by one with different speed in different directions. Later he free himself and took a motobike with extra seat. Now he can follow footprints and pick up one prisoner at a time and bring them back to jail. Each prisoner moves with constant individual speed v_i and left the jail at time t_i. In which order the guard should bring the prisoners back in order to minimize the time?

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?