“…nd of an ideal, massless spring k,pa-through poi-rORSP, md mpeating Aman. .wci
ID: 1515105 • Letter: #
Question
“…nd of an ideal, massless spring k,pa-through poi-rORSP, md mpeating Aman. .wcilws at the end of an ideal,-less A ine tnQ the mass is neleased at point @ (wherA ndv 0). You do NOT need so show your work for she c.2pa) Find the mass's displacement at-70 d.(2ps.) Fiad the honiz. component of mass's velocity atrn70s sil-in dhe Niank eestios,bu be sure so inclade wnits, appropriate e siges, and appropriate sig appropriate sig fes! ± signs, e.(2ps) Find the horiz.component of the mass's acceleration at- 70s 2 3 ps) Suppose thae nild friction and air resistance cause the amplitude of oscillations to diminish gradually over-ne. sinking hom 100to50cm. Find total energy dispated by friction over this time iod. Show yeur wortExplanation / Answer
2. (a) T = 2pi * sqrt(m/k) = 1/f
= 2pi/T = sqrt(k/m)
T = 2*3.14*sqrt(1.3/5.5) =3.0449 Sec.......................Ans.
(b) x(t) = Xmax * cos(t + phi)
v(t) = -Xmax * * sin(t + phi)
v(t) = -10.0 cm *2.062* sin(2.062t + phi)
Vmax = +/- Xmax * = 1*2.062 =2.062 m/s.........Ans.
(c) x(t) = Xmax * cos(t + phi)
x(7) = -10.0 cm*cos(2.062*7 +0) =19.36 cm.........Ans.
(d) v(t) = -Xmax * * sin(t + phi)
v(7) = -10.0 cm*2.062*sin(2.062*7) = 0.51398 m/s
(e) a(t) = -Xmax * ^2 * cos(t + phi)
a(7) = -1.0*2.0622*cos(2.062*7) =4.117 m/s2.............Ans.
(f) F = ma = 1.3*4.117 =5.352 N
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