Question

11.3 The vertical motion of mass A is defined by the relation x = cos(101) - 0.1sin(10t), where x and t are expressed in mm and sec- onds, respectively. Determine (a) the position, velocity, and acceleration of A when t = 0.4 s, (b) the maximum velocity and acceleration of A.

Answer 1

s fra en 'mm', 't's en 's' ie see Geven, dt 12 Cos Clot) - 0.1 Bin Clot) (1) Position = ()cos 10t -0.1 Sin clot) at t=0.4 See ,u = COS (4) - 0.1 Bin (0.4 - 0.991 mm (10) Velocity (V) - dx of 'ou =) V: d{cos (10t) - 0.1 Sin (10t)} 1 de V. -10 Sin (10 t) - cos (101) at t = 0.4 see, V.,-10 Bin (41)- Cos 4 JV-1.695 mm/seel 011) alieleration ca), dv d of H dels as f-10 sin ciot) - cosciot)} :-) a =-100 COS(10t) + 10519(104)lo sin (lot) - 100 cos Clot) ielt t= 0.4 see, Ta :-99.059 mm/see?!

Maximum velocity occo velocity occurs when Queleration [()=0] 0 a 10 Sin (lot) - 100 costou) - 0 5) 10 Son (10 t) = 100 cos pot) tan (106) - 10 2) 10t: tani' (10) to tan (10) + 0.1471 Brittany Set. -0 (do in radian) Maximum aueleratio Oculo duele ratio occurs when Jerk(s) (s a:10 Sen Clot) -1oo costot) oldu - 100 COS (10 t) +1000 Gin (10t): 0 = 100 cos (106) -1000 sm (ot) tan clot) : 100 - to tan' (to) , #61351food porn 10 -0.00996 (O) (0.00996+1) enot possible) so, t = 3.1316 2 see - 0 * from ea 0 Vmax ocum ou (t = 0.1471 see] So Vmax V-10 bin (0.1471410) - cos C1o x 0.6471) l Vimax = (-) 10.0499 (mm/sec) and From ed) Amar Occus at (t : 0.0099648 -3.13162 see $o amorsa 10 ech C10x3.13162) - 100 cos (10x3.13162) amasa (-) 100-499 mm/see] P .VN

Shortcut for Vimas Vaflo SO (ROE) -16 05 (10 t) Vimana v 6-10° +60)7 , 40.64 mysel (EXTRA) Short cut for amar a: son clot) -100 cos Clot). Puideli amax - 102+(-100² 2 100.49 mm/seed (*) co-efficient. additem and Square groot
SUMMARY:Key points;Shortcut is valid only in magnitude.

Jerk :Jerk is the rate at which any mass's acceleration changes with respect to time i.e derivation of acceleration.

-Any equations maximum occurs at it's one degree higher derivative=0

-During calculation of (v)max or (a)max always calculate in "radian" and if time 't' comes in negative add 'pie' to it as time can not be negative .By adding "pie" we get the same value as it is occurring in cycle.