Question

Version 3 Part D Rotational Dynamics and Oscillations) Problem D1: The displacement of a particle is given by x(t) = 0.03 sin (2010+ meters 1) What is the angular velocity of the particle? 2) What is the period of the particle? 3) What is maximum displacement? 4) What is the maximum speed? 5) What is the maximum acceleration? 6) What is the position of the particle after 1s ?

Answer 1

xlt) = 0'03 sin (202t + 7 ) m stondared wave caun is xlt)A sin (Wt I kv) on comparing | W = 20x sadis 2) time period T = 27 sec. T= 22 -I sec. - Zon 10 T= oil sec [T= 0.1 sec] xlt)= 0.03 sin ( 20 at tha). 3 as maximum value of sine is a maxi = 0'03 x1 = 0'03 metal 4) 2(t) = 0.03 sin (200++ ) differentiate worit t e U= dx = 10:03) (20x) (as (20 26 tu -

yoo v - maximum cas (2341%)=) so v-(0.03)( 262 ) x (1) m Toto ostmis u= 0.67 m/s = v= 1.88 mis 5) v = (0.03) (207) cas (zoat + hu) acceleration = Q = dve =-(0'03) (20x) Slny (203t+W) so for maximum, sineal az - (0.03) (202)2 (-1) la= 118.30 m/s² alt) = 0.03 sin ( 20 2t +W). at t=1s 211) = 0.03 sin ( 207+ yu) = 0.03 sin ( 2x410)+ yu) sin (anato) = sino 2(1) = 0.03 sin (7) x1) = 0.03 m = 0.021 m. 2