Question

A particle is oscillating on the c-axis about the origin. It passes through the point A, where r = 0-01 metres, with speed 0:09 m/s and it passes through the point B, where x = -0.02 metres, with speed 0.06 m/s. (a) Show that the amplitude of the motion is metres. (b) Show that the motion has period 3 seconds. (c) Find, correct to the nearest hundredth of a second, the time that the particle takes to move directly from A to B.

Answer 1

Solm Let particle movement of oscillation defined by the expression a(t) = A sin (wt) t=0, x10=0 it's oscillating about the x=0.01 m xelt=0.09 m/s at ti x=-0.02 m xl (t) = 0.06 m/s. attz orgin 1 da dt Aw wswt => -(1) oile 3 2 tati Aw wosk til = 0.09 0-06 Au ws(wtz)= ---(2) tatz sin(uti) = 0.21 sin(wtz) = -0.02 AI А (1)-(3) wswt 1) cos (Wto) Ti sintuti 를 Il sin utz) 4A²410-01) 9A? 9 10.02 galA= 4.9.(001) – 410.01) 5 A² 410.017².8 2.0.01.18 hola 55 0012 . - ) A2 - 9 1- €0.02² AL = > A= 25 IS (о A - 0-0 (5) 1 AW 125 sinkwt ) = 0 cos(wti) = 0-09 sintut)t coswt) = 1 (0.002 (0.09² + = 1 AL AL wz

+ ५.- 10 2 100 cross (0-000- (0.05) (१२) (१२) + (RS -) - + १ (-11b sizle) 100-125-२६)(225) 1002२॥ me titiply Peloste Loo + lowa 12-2-। -10+ १ + (0 70001 12-2 (25 -) (o (Du- -18+45 25 SO low S) %3D 2 59 27 20 2TR - period T= नि ७) 4-.-4 (570-01-51903 )) 1 s ( sint 0-01 - Sin-(-0-02 -TO/125 -4110/1Rs), 0.34034 sec.

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