Question

LUumeu. wwe. 1. Mass-spring system [20] A 0.50 kg mass is connected to a 5.0 N/m spring. From the rest position (x = 0), it is set into motion with an initial speed of +2.0 m/s. (a) What is the amplitude of the subsequent oscillatory motion? [5] (b) How long will a complete oscillation take? [5] (c) What will be the position and the velocity of the mass at t=0.30 s? [10]

Answer 1

S solution! mars , m = o.sorg Skering constant, k= 5.0 N/m xo)=0 S eco) = +2.omis As we know for such sperity maus system xlt)= A sin lut + o) & ult)= Aw les(ut to) here, wat = rs = do = 3.16 radis Now, x(0) = A sin (6) vlo)- A w ees (6)= Aw. @ 0= Asino) 2 - Aw = A (3.16) but A tO .. (6=0] A = 0,63 meter. is the revered amplitude 16) Time period, T = 20 m = 263.140.5 (T=1.90 sec regulered time. C) At t = 0.3 sec x (0.3) = (0.63) sin (3.168 0.3) = 10.01 m) (0.31 = 60.63) (3.16) bor (3.16 * 0,3) = 11.99 m/s/ v s