Suppose a water tower in an earthquake acts as a mass-spring system. assumethat the container on top is full and the water does not move around. the container then acts as amass and the support acts as the spring, where the induced vibrations are horizontal. suppose thatthe container with water has a mass of m = 10; 000 kg. it takes a force of 1000 newtons to displacethe container 1 meter. for simplicity assume no friction. when the earthquake hits the water toweris at rest (it is not moving).suppose that an earthquake induces an external force f(t)=ma\omega ^2cos(\omega t) .a) what is the natural frequency of the water tower? b) suppose a = 1 and an earthquake with frequency 0.5 cycles per second comes. what is theamplitude of the oscillations? suppose that if the water tower moves more than 1.5 meter from therest position, the tower collapses. will the tower collapse?