Question

Round to two decimal places if necessary. A spring is stretched 10 centimeters by a 13 N weight. The weight is then pulled down an additional 3 centimeters and released. Neglect damping. Find the function (1) for the position of the spring at any time t.

Answer 1

fa further 3cm BN Loom and then left uits Find un position of sprung at any time 't As the spring Also constant for this particular spring force mof (mas a spring) = 1/4 = 13 - 13 kg 13 = 113 w/ rom = 13 = 13 NIM 19. now condition at the further Streching ma+ku = 0 moun + KU = 0 Equillibrium a= d'u att * 13 u"+ 13 u zo ulo) = 3cm ulo)zo Now for solution of this diff Equation. 1.326 ""+ 13 u o u" + 13 u o 1326 u" + 9.8u =0 How for comply Roots: 0²+ 9.8 =0 = = 59.8 = 13.13 i the defination diff equation GENERAL SOLUTION utt) = Cicos (3.13) + + Sin (3.13) As 40) = a + Co.o = 3 6=3 4'(o) =0, nah akin 3.13t) + (2 los (3.13) (3.13) 3.13 ulo) = 0 + C2 (0) 22-0 los 3.13+) Tuch 3 or Julh = 3 los sanont a As ss1 grawit