A mass 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 and the motion stops when the mass hits the ground at z = 0. (You don't need U(x, y, z) 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 where the amplitudes A, B and the phase difference Given A = 1, B = 2,6 = /3,w= 0.5, and g = U(x, y, z) = - k(x 1/2 k(x + y) + mgz t_contact 1.430 X_contact 0.755 Y_contact -0.380 z_contact = x(t) = A cos(wt) y(t) = B cos(wt + p) = z(t) = - 1 29t 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, y0, z0], [x1, yl, zl], [x2, y2, z2], ...]. 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) 0; = - + 20 3. stores the time for hitting the ground (i.e., the first time t when z(t) 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print are determined by the initial conditions, and the frequency is w = k/m. 9.81, write a program that (Output floating point numbers with 3 decimals using format (), e.g., "t_contact partial example output above is for zo = 10. = {:.3f}" .format(t_contact).) The