Question

4. A mass weighing 4 lb stretches a spring 1.5 in. The mass is given a positive displacement of 2 in from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of 2 cost 3t lb, formulate and solve the initial value problem describing the mat of th

Answer 1

äolution: determine the position os time t. u na ting tinus (7) 4 lb ga 22 ft lose? 4 wlog 옳 -100 8 = 0, dit) = (1050)? La 1.5 in 1.5 ft - ift 6 Inc. K 2 mg ZE CE 4x8 equa trón () becomy 2 Cos 31 + 32u - 00)- 8 ☺ u" +256 l = 16 cos 3 initial condition U10): 2in 12 u10) - o auxillary dastofa not onts efon + zu 256-0

cos ibt + ₂ sin 16t 16 cos 3t 16 cos 36. DP 56 247 general Solution is. 16 COS 30 247 Ult) = C cos 16+ 7 Czsin 16 + + 16 - 41 (0) - C, + 247 15) 1486 l'10) = 0 .then hence, the general solution ig. ult) = 131 cos 16t 16 + cos at 2427 1482 the graph of displacement u versus tume mer voors -ool -0.24 time (ge)

Hoonal Joyces f/2) = usinot when resonance OCCUS 09 pos 91 - u"+ 256 illa 32 Jinot P. 32 sinot D?+ 256 32 Sinot -w24 256 w 16 f! - + 256 - 0 2) 16 sad I sec. thank you, plz date.