Investigation of Simple Harmonic Motion There are two common forms of the equations used to model simple harmonic motion (SHM), which is the motion of springs, swings, tides, and many other periodic phenomena. These equations are y(+) = A sin(wt + $) and y(t) = casin wt + cicos wit. where: (t) = distance of weight from equilibrium position w = angular frequency (measured in radians per second) A = amplitude * = phase (depends on initial conditions) C1 = Asing C2 = Acost Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation U will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion ( website. You are given the equation y(+) = 2 sin dat + 5 cos 4at. which models the position of the weight, with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form. y(+) = A sin(wt + +). Part A Use the information above and the trigonometric identities to prove that A sin(wt + $) = cysin wt + cicos wit. BIUXX , 15px Space used (includes formatting): 0 / 15000 Part B To rewrite y(+) = 2 sin 4xt + 5 cos 4at in the form y(+) = A sin(wt + *). you must first find the amplitude, A. Use the given values C1 = A sing and C2 = A cosd, along with the Pythagorean identity, to solve for A. BIUXX , 15 px Space used (includes formatting): 0 / 15000 Part C To rewrite y(#) = 2 sin 4xt + 5 cos 4at in the form y(t) = A sin(wt + ). solve for $ Show your work and solution in the response box. BIUXX, 15px Space used (includes formatting): 0 / 15000