Question

A mass that weight 14lb stretches a spring 1 in. The system is acted on by an external force 7 sin(8V6t) lb. If the mass is pushed up 1 in and then released, determine the position of the mass at any time t. Use 32 ft/s? as the acceleration due to gravity. Pay close attention to the units. u(t) = in

Answer 1

Evaluate the particular sol using method of undetermined coefficient Olt) At cos (5384 Ð + Bt sin ( 53849 N'(U) - Acos(83844) + 384 At som (13841 +13 sin (13829 + $384 Bteng (wagut) eigen uit) Asint cresch hohlag - Boy Asin (1354 +) – JBxua són (138u+) – 384. Atsin (1384 +) + 1384 Beog (1334t 384 Beos (1389+ )- 384 Btsin (1384 +) + -21384 Asin (5384 +) - 384At sin (szaut) + 2 J38u8cos (J38u+)– 384 Bk sin(izsut) Substitute in original equat. simbio tas no olles -Q1384 Asink 384+)- 384 Atsin 384 +) +25384 Boos (1384t) .384 Btsin 38ut +2688 (At 60s (1384 +) +87 sin (13847 ) = 112 sin (860) CS Scanned with CamScanner

-141384 A Sim 1384 t) + 14 3384 BcOS (1384) + = 112 sin (Bf6+) √384 = 886 52 Jea AH - 112 86 Asin (886t) + 112 56 B cos (886) to = 112 sin (886) =) A = -1 - 11256 A = 112 ro Jos kot2b - B=0 tazesant Ut) = -t cos (886t) 6 u su, tult) u =( cos(8rot) + (q sin (8567) Cocos (8rot) ula-8866, sin (886t) +856 (2 cos (8rot) & sin(886t I cos(886t) the r6 alo) ullo) ㅗ 12 C₂886 - 11/6 ) 1 C to -0 = 12 C2 a 1 12 1 48 CS Scanned with CamScanner

12 ub) - I cos (816+) tute sin (864) cos/856+) V6 Thus the position of mass at any time is 48% cost8ft) & fodin 46 cos(866t) + To sin (866t) - 48H cos(866 + 48 56 ft tis in seconds - 456 cos (8f6) + fesin (8f6t)-u8 tcos(860+). in uro nie alakal st CS Scanned with CamScanner