Question

2. -15 points SerPSE 10 15.2.0P.003. My Notes In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 8.00 cos (32 +) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t = 0, find acceleration of the piston. cm/s2 (d) Find the period and amplitude of the motion. period amplitude Need Help? Read It Watch

Answer 1

Solution given: A piston ascillates with simple harmonic motion and its position given by - here'n'in com n = 8.00 Cos (3t+r At t=o. Position of pistion from equation (1) 21= 8.00 (03/3X0+)= 8.00Carl 225.66 cm ) (6) We know that velocity v=d[rootas131*.) d ſ dcostat). -asino v --24.00 sin(3t+ )-@ 1 dt Atot-o V = - 24.00 Sin (3807) 1 = -16.97 cm/s/

[C] We know that acceleration a= dr dt forom equation (2) ao d[-24.00 Sin (37 +5I) a - 72.00(99134+2) Asincat). a cascat) At t=0 a = -12.00 (as [340 +F) - - 72.00 (01/12) a = - 50.91 cm/s? We know that equation of SHM is - A Concwt + p) - 3 where A is amplitude and w in angular fou quenry and ø is initial phase compare equation (1) and (3) A = 8.00cm) and w = 3 rad's W = 24 - 7 - 2017 - {n 77 = 2.095] τη ροηγοί / oscillation