Please explain this in easy to understand terms- with steps from the top

I. Alternating Current (33pts total:5ptseach, +3ptsforbeingyow). Imagine an electrical current which comes out of an American wall outlet in a smoothly alternating pattern of high current in one direction down in magnitude all the way through zero to equally high current in the other direction, and so on forever. This alternating current, is measured in Amperes and designated with a variable called /, fluctuates AROUND an EQUILIBRIUM value of o Amperes according to the following equation (for which time is measured in seconds): = -1421291. Imagine, further, some wall device for which the current at t=o (the initial and maximum current ) is 6 = +15 Amperes. In HERTZ (rounded to 3 sig figs). approximately how frequently does this I) device cycle through the full range of total charge magnitudes (from its maximum, through o to its minimum, and all the way back through o to its initial/maximum)? DON'T FORGET TO PROVIDE SOME KIND OF DIAGRAM! In seconds, find how much TIME will elapse from =0 until precisely the 2) second instant the current is running at a maximum value but in the negative direction (the second time, as measured from t= 0, that the current reaches l = - 15 Amperes). You may round to something like 3 sig. figs. 3) a) In Amperes per second, find the instantaneous rate at which the current changes with respect to time at the very first instant the current value is I=0 Amperes. You may round to something like 3 sig figs. b) At this moment (described above), explain whether the current is growing increasingly negative, increasingly positive, decreasingly positive or decreasingly negative. Thoroughly and convincingly explain how you know. HINT for both the above. Whenever we talk about an 'instantaneous rate', we are talking about a derivative, no? Yes. 4) Assume that the whole phenomenon/experiment is re-done with all the same p. 4 of 7 given equations and values EXCEPT: This time / = -45 Amperes (instead of +15 Amperes). Provide answers to ALL the above three questions under these new conditions. You can re-calculate and/or provide verbal explanations, but you must fully explain how each of your above three answers does or does not change. ") TRUE or FALSE and SHOW WHY!: 1 =+ 45 cos [377 + + (pi)) is "A SOLUTION" to the Dif. Equation AND the new condition 6 = -45 AII Toque-Tocque(33 pts:5 pts each piece, +3 for being you). Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like it does here, but provides a different and (as yet) unknown constant value for free-fall acceleration. There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d20 dt2 = -250. Here, 0 refers to an angular displacement measured from the vertical and f refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0 = (/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, @= (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. ii. Approximationg the number of Hertz to three significant digits if necessary, what is the standard frequency of this oscillator on a string? ili. Approximationg to three significant digits if necessary, how many seconds should we expect this pendulum to take in order to get from one turning point to its equilibrium position (to a fully vertical orientation)? iv. What is the particle's approximate SPEED at t = /4 seconds? (for which T stands for 'Period' of this pendulum). P. 6 of 7 v. Break up your pure FBD into components. Given your component diagram, Show how the angular frequency for a pendulum is determined fully by parameters: That is, show that harmonic oscillation will occur at a rate which depends on the length of the string and on the free-fall acceleration constant due vi, to gravity. According to your finding in v (above), determine the value for g at the location this pendulum swings. Go back to part iv, above: Show how you can use this finding for g to compute a numerical value for speed at t = 7/4. SHOW how two distinct solution methods can serve to check one final numerical answer for instantaneous speed at t = T/4.IV. PULSE (33 pts ) Show how the propagation of WAVES can be understood as a properly arranged collection of properly phase-staggered harmonic oscillators. A) Clear, detailed and fully labeled diagrams: 9 pts B) Clear, correct and persuasively presented mathematical equations : 9 pts C) Clear, detailed and thoughtfully crafted verbal explanations: 9 pts D) Clear and final conclusion, centered on one final equation with every term somewhere explained: 6 pts Page 7 of 7