17.5 Dropped 2D harmonic oscillator This lab will be available until January 31st, 11:59 PM MST Amass m is held by two perpendicular identical springs in space in the x-y plane and is dropped from a height zo under the influence of gravity (let's call this the "dropped 2D harmonic oscillator"). The mass moves in a potential U(x, y, z) = 3k(x2 + y2) +mgz and the motion stops when the mass hits the ground at z = 0.(You don't need U(2, , 2) for solving the problem and it is only provided for the exact physics context.) The trajectory of the mass, i.e, its curve in space, r(t) = (x(t), y(t), z(t)) is x(t) = A cos(wt) y(t) = B cos(wt + o) 1 z(t) = - + zo 2 59t? Vk/m. where the amplitudes A, B and the phase difference o are determined by the initial conditions, and the frequency is w= Given A = 1, B = 2,0 = 7/3,w = 0.5, and g = 9.81, write a program that 1. reads the initial drop height zo from user input; 2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[x0, yo, 20], [x1, yl, zl], [x2, y2, 22], ... ). Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t)