(1 point) A spring with a 4-kg mass and a damping constant 4 can he held stretched 2 meters beyond its natural length by a force of 4 newtons. Suppose the spring is stretched 4 meters beyond its natural iength and then released with zero velocity, In the notation of the text, what is the value 02 drink? I 16 I' mgkggfsee2 Find the position of the mass, in meters: after t seconds. Your answer shouid be a function of the variable t with the general form clam cosht] + 023?: sin(t} a : '40 | ,3 : |I sqrtsr2 l 1r = '42 I| 6 = | sqrtsrz I Cl: 0 l 62=|I4 II ['l pointjAspring with a Qkg mass and a damping constant 19 can be held stretched 1 meters beyond its natural length by a force of 4 newtons. Suppose the spring is stretched 2 meters beyond its natural length and then released with zero velocity. In the notation of the text: what is the value c:2 4mk? 1112ltiggfsec2 Find the position of the mass, in meters: aftert seconds. Your answer should be a function of the variable t of the form c1 .95\" + c2 am where a = {the larger of the two) = (the smaller of the two) C1 = C2 [1 point) Suppose a pendulum with length L (meters) has angle 9 [radians] from the vertical. It can be shown that 8 as a function of time satisfies the differential equation: (126 g_ where g = 9.8 mr'seclsec is the acceleration due to gravity. For small values oft? we can use the approximation 5111(9) m .9, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion ofa pendulum with length 1.5 meters and initial angle [)2 radians and initial angular velocityr d/dt 0.2 radiansi'sec. B. At what time does the pendulum first reach its maximum angle from vertical? {You may want to use an inverse trig function in your answer) seconds (3. What is the maximum angle (in radians} from vertical? D. How long after reaching its maximum angle until the pendulum reaches maximum deection in the other direction? (Hint: where is the next critical point?) seconds E. What is the period of the pendulum, that is the time for one swing back and forth? seconds