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In fortran for linux. Using the Velocity-Verlet method describe the motion of a pendulum subjected to a force extra due to a spring as shown in the figure: The equation of motion of the pendulum is: (@)si ) sin(@) – 6) (4) *1966 g@ tg(0) = a With dw a = dt M W = de dt Consider: m-1, L-1, k-1 and h-Un, where n- an integer greater than 1. For example: h-1/2 and simulate the system for a total of 100 s with a 8-0.15. Initial conditions: w = 0.0 and give 45 and 180 degrees as initial data. 1- Calculate the data to graph (t),w(t). 2- Calculate the period of oscillation 3- Is the new period greater or less than in the case without spring and small angles? Show your result