4.18. T =n1/ mlIF = 0.2 s.
4.19. T =2:t y (1-1)=1.1 s.
4.20. T = 2 1/ llg[3112+arcsin(a/13)].
17 2 — where =
4.21. t
u'h
1— 1/-1 —
4.22. T = 4rcm/pgr^2 = 2.5 s.
4.23. T =2n1/ ri (1 — 11) mix 0.13 s.
4.24. T = 2n V m/(xi ± x2).
4.25. T = 2aV mix, where x = x1x2/(t1 x2)-
4.26. co = 1/ 2To /m/.
4.27. T = 2n V m/Spg (1 + cos 0) = 0.8 s.
4.28. T =n1/ 211kg = 1.5 s.
4.29. (a) x (gIR) x = 0, where x is the displacement of the
body relative to the centre of the Earth, R is its radius, g is the
standard free-fall acceleration; (b) i = IG VRIg =^42 min,
(c) v = 1/ gR = 7.9 km/s.
4.30. T = 25tV 111 g — w = 0.8 s,^ where^ jg— wl =
=1/ g 2 ± W 2 - 2gtv cos [3.
4.31. T —27t/V xlm — (0^2 = 0.7 s, co> xim 10 rad/s.
4.32. k = 4n 2 a/gT 2 = 0.4.
4.33. (a) 0 = 3.0° cos 3.5t; fring
(b) 0 = 4.5° sin 3.5t; (c) 0 = 15
= 5.4° cos (3.5t + 1.0). Here t
is expressed in seconds. (^) W -
4.34. F = (m 1 ± m 2 ) g
miaco 2 = 60 and 40 N.^ 0.5 -
4.35. (a) F =mg (1+^ )
±-cioig— cos cot), see Fig. 30;^2 a^ 22"4^ w t
(b) a
m in
= g/w^2 = 8 cm; (c) a =^ Fig. 30.
= l/2h/g— 1) co g/co 2 = 20 cm.
4.36. (a) y = (1 — cos tot) mglx, where co = Vx/m; (b) Tmax --=
= 2mg, Tmin = O.
4.37. (xlro) 2 + a (y/v 0 ) 2 = 1.
4.38. (a) y = (1 — cos cot) who^2 ; (b) y = (cot — sin (et) We.
Here co
4.39. Ahmo. = mglk = 10 cm, E = m^2 g^2 /2k = 4.8 mJ.
4.40. a = (mg/x) V 1 +2hxlmg, E = mgh + m^2 g^2 /2x.
4.41. a= (mglx)1/1 +2hx1(m+ M)g.
4.42. Let us write the motion equation in projections on the
x and y axes:
x = coy, y = —cox, where co = alm.
325