āϏāĻŽā§āĻāϰāĻŖ |
āĻĒā§āϰāϤā§āĻ āĻĒāϰāĻŋāĻāĻŋāϤāĻŋ āĻ āĻāĻāĻ |
ā§§.āĻĒā§āϰāϤā§āϝāĻžā§āύ⧠āĻŦāϞ,F = -Kx
⧍.āϏāϰāϞ āĻāύā§āĻĻāĻŋāϤ āĻāϤāĻŋāϰ āĻā§āώā§āϤā§āϰ⧠: āĻāϤāĻŋāϰ āϏāĻŽā§āĻāϰāĻŖ : āϏāϰāĻŖā§āϰ āϏāĻŽā§āĻāϰāĻŖ : x = Asin (Īt+δ )
ā§Š.āĻā§āϞāĻŋāĻ āĻŦā§āĻ,
ā§Ē.āĻĻā§āϞāύāĻāĻžāϞ,
ā§Ģ. āĻāĻŽāĻĒāĻžāĻā§āĻ : ā§Ŧ. āĻŦā§āĻ : ā§. āϤā§āĻŦāϰāĻŖ : a = - Ī2A ā§Ž. āϏāϰā§āĻŦā§āĻā§āĻ āĻŦā§āĻ :vmax = ĪA ⧝. āϏāϰā§āĻŦā§āĻā§āĻ āϤā§āĻŦāϰāĻŖ :amax = Ī2A ā§§ā§Ļ. āĻāϤāĻŋ āĻļāĻā§āϤāĻŋ :k = ÂŊ K (A2 â x2) ā§§ā§§.āϏā§āĻĨāĻŋāϤāĻŋ āĻļāĻā§āϤāĻŋ :U = ÂŊ kx2 ⧧⧍. āϏā§āĻĒā§āϰāĻŋāĻā§ā§āϰ āĻĻā§āϞāύāĻžāĻāĻžāϞ : ā§§ā§Š. āϏā§āĻĒā§āϰāĻŋāĻā§ā§āϰ āĻŦāϞ āϧā§āϰā§āĻŦāĻ :K = mg /I ā§§ā§Ē. āϏāϰāϞ āĻĻā§āϞāĻā§ āĻĻā§āϞāύāĻāĻžāϞ : ā§§ā§Ģ. āĻĻā§āϞāύāĻāĻžāϞ : T = I /n
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F = āĻĒā§āϰāϤā§āϝā§āύ⧠āĻŦāϞ K = āĻŦāϞ āϧā§āϰā§āĻŦāĻ x = āϏāϰāĻŖ A = āĻŦāĻŋāϏā§āϤāĻžāϰ t = āϏāĻŽā§ Î´ = āĻāĻĻāĻŋ āĻĻāĻļāĻž Ī = āĻā§āĻŖāĻŋāĻ āĻāĻŽā§āĻĒāĻžāĻā§āĻ m = āĻāϰ T = āĻĻā§āϞāύāĻāĻžāϞ v = āĻŦā§āĻ a = āϤā§āĻŦāϰāĻŖ g = āĻ āĻāĻŋāĻāϰā§āώā§ā§ āϤā§āĻŦāϰāĻŖ l= āĻĻā§āϰā§āĻā§āϝ L = āĻĻā§āϞāĻā§āϰ āĻĻā§āϰā§āĻā§āϝ n = āĻāĻŽāĻĒāĻžāĻā§āĻ
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āĻāĻžāĻŖāĻŋāϤāĻŋāĻ āϏāĻŽāϏā§āϝāĻž āĻ āϏāĻŽāĻžāϧāĻžāύāĻ
- Magic â T1/T2 = â(g2/g1) = (86400-x)/(86400)
â R/(R+h) = â{(R-h)/R} = â(L1/L2)
- āϞāĻŋāĻĢāĻā§āϰ āĻā§āώā§āϤā§āϰā§, āύāĻŋāĻā§āϰ āĻĻāĻŋāĻā§, T = 2Ī â{L/(g-t)}
āĻāĻĒāϰā§āϰ āĻĻāĻŋāĻā§, T = 2Ī â{L/(g+t)}
ā§§. 30Nm-1 āϧā§āϰā§āĻŦāĻā§āϰ āĻāĻāĻāĻŋ āĻāύā§āĻā§āĻŽāĻŋāĻ āϏā§āĻĒā§āϰāĻŋāĻ āĻāϰ āĻāĻ āĻĒā§āϰāĻžāύā§āϤ āĻāĻāĻāĻŋ āĻĻā§ā§āĻžāϞā§āϰ āϏāĻžāĻĨā§ āĻāĻāĻāĻŋā§ā§ āĻ āĻĒāϰ āĻĒā§āϰāĻžāύā§āϤ⧠0.5kg-wt āĻāĻāύā§āϰ āĻāĻāĻāĻŋ āĻŦā§āϞāĻ āĻāĻāĻāĻŋā§ā§ āϏāĻžāĻŽā§āϝāĻžāĻŦāϏā§āĻĨāĻžāύ āĻĨā§āĻā§ āĻāĻāĻāĻŋ āĻāύā§āĻā§āĻŽāĻŋāĻ āĻāϰā§āώāĻŖāĻšā§āύ āĻā§āĻŦāĻŋāϞ āĻŦāϰāĻžāĻŦāϰ 10cm āĻā§āύ⧠āĻā§ā§ā§ āĻĻā§ā§āĻž āĻšāϞ⧠āĨ¤ āĻĢāϞ⧠āĻāĻāĻŋ āϏāϰāϞ āĻāύā§āĻĻāĻŋāϤ āĻāϤāĻŋāϤ⧠āϏā§āĻĒāύā§āĻĻāĻŋāϤ āĻšāϤ⧠āϞāĻžāĻāϞ āĨ¤
(i) āĻŦā§āϞāĻāĻāĻŋāĻā§ āĻā§ā§ā§ āĻĻā§āĻā§āĻžāϰ āĻĒā§āϰā§āĻŦ āĻŽā§āĻšā§āϰā§āϤ⧠āĻāϰ āĻāĻĒāϰ āϏā§āĻĒā§āϰāĻŋāĻ āĻāϰā§āϤā§āĻ āĻĒā§āϰāϝā§āĻā§āϤ āĻŦāϞ āĻāϤ?
(ii) āĻŦā§āϞāĻāĻāĻŋ āĻā§ā§ā§ āĻĻā§āĻā§āĻžāϰ āĻĒāϰ āĻĒāϰā§āϝāĻžā§āĻāĻžāϞ āĻāϤ?
(iii) āĻāϤāĻŋāϰ āĻŦāĻŋāϏā§āϤāĻžāϰ āĻāϤ?
(iv) āĻĻā§āϞāĻžā§āĻŽāĻžāύ āĻŦā§āϞāĻāĻāĻŋāϰ āϏāϰā§āĻŦāĻžāϧāĻŋāĻ āĻāϤāĻŋāĻŦā§āĻ āĻāϤ?
(v) āĻŦā§āϞāĻāĻāĻŋāϰ āϏāϰā§āĻŦāĻžāϧāĻŋāĻ āϤā§āĻŦāϰāĻŖ āĻāϤ?
(vi) āĻŦā§āϞāĻāĻāĻŋāϰ āĻŽāϧā§āϝāĻžāĻŦāϏā§āĻĨāĻžāύ āĻĨā§āĻā§ āĻāϤāĻŋāĻĒāĻĨā§āϰ āĻĻāĻŋāĻā§ āϝāĻāύ āĻ āϰā§āϧāĻĒāĻĨ āϝāĻžā§ āϝ⧠āĻŽā§āĻšā§āϰā§āϤ⧠āϤāĻžāϰ āĻŦā§āĻ, āϤā§āĻŦāϰāĻŖ, āϏā§āĻĨāĻŋāϤāĻŋāĻļāĻā§āϤāĻŋ āĻ āĻāϤāĻŋāĻļāĻā§āϤāĻŋ āĻŦā§āϰ āĻāϰ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
(i) F = -kx = -30Ã(10/100) = -3N [ans.]
(ii) T = 2Īâ(m/k) = 2Īâ(.5/30) = 0.81s [ans.]
(iii) A = 10cm = 0.1m [ans.]
(iv) Vm = AĪ = A.(2Ī/T) = .1Ã(2Ī/.81) = 0.77ms-1 [ans.]
(v) am = Ī2A = (2Ī/T)2ÃA = (2Ī/.81)2Ã.1 = 6 ms-2 [ans.]
(vi) V = Īâ(A2-x2)
= (2 Ī/.81) â(.12-.052) = .67ms-1 [ans.]
āϤā§āĻŦāϰāĻŖ, a = Ī2x = (2Ī/.81)Ã.05 = 3ms-1 [ans.]
āĻāϤāĻŋāĻļāĻā§āϤāĻŋ, T = ÂŊ mv2 = ÂŊ à .5 à .672 = .112J [ans.]
āϏā§āĻĨāĻŋāϤāĻŋāĻļāĻā§āϤāĻŋ, U = ÂŊ kx2 = ÂŊ à 30 à .052 = 0.038J [ans.]
⧍. āĻāĻāĻāĻŋ āϏāϰāϞ āĻĻā§āϞāĻ 2 āĻŽāĻŋāύāĻŋāĻā§ 60 āĻŦāĻžāϰ āĻĻā§āϞāύ āĻĻā§ā§ āĨ¤ āĻĻā§āϞāĻāĻāĻŋāϰ āĻĻā§āϰā§āĻā§āϝ āύāĻŋāϰā§āĻŖā§ āĻāϰ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
T = 2Īâ(L/g)
â L = (gT2)/(4 Ī2) =
â´ L = 0.993m [Answer]
ā§Š. āϏāϰāϞ āĻāύā§āĻĻāĻŋāϤ āĻāϤāĻŋ āϏāĻŽā§āĻĒāύā§āύ āĻāĻāĻāĻŋ āĻŦāϏā§āϤā§āϰ āĻŦāĻŋāϏā§āϤāĻžāϰ 0.01m āĻāĻŦāĻ āĻāĻŽā§āĻĒāĻžāĻāĻ 12Hz āĨ¤ āĻŦāϏā§āϤā§āĻāĻŋāϰ āϏāϰāĻŖ 5Ã10-3 āĻšāϞ⧠āĻāϰ āĻāϤāĻŋāĻŦā§āĻ āĻāϤ?
āϏāĻŽāĻžāϧāĻžāύ :
V = Īâ(A2-x2) Ī = 2Īn
= n = 12Hz
â´ V = 0.654ms-1 [Answer] A = .01m
x = 5Ã10-3m
ā§Ē. āĻā§āύ āĻāĻāĻāĻŋ āϏā§āĻā§āύā§āĻĄ āĻĻā§āϞāĻā§āϰ āĻĻā§āϰā§āĻā§āϝ āϝāĻĻāĻŋ 1.44 āĻā§āĻŖ āĻŦā§āĻĻā§āϧāĻŋ āĻāϰāĻž āĻšā§ āϤāĻžāĻšāϞ⧠āĻāϰ āĻĻā§āϞāύāĻāĻžāϞ āĻāϤ āĻšāĻŦā§?
āϏāĻŽāĻžāϧāĻžāύ :
T1/T2 = â(L1/L2) T1 = 2s
â T2 = T1â(L2/L1) T2 = ?
= 2â1.44 L2 = 1.44L1
â´ T2 = 2.43s [Answer]
ā§Ģ. āĻāĻāĻāĻŋ āϏāϰāϞ āĻĻā§āϞāĻ 0.9s āĻ āĻāĻāĻŦāĻžāϰ āĻāĻŋāĻ āĻļāĻŦā§āĻĻ āĻāϰ⧠āĨ¤ āĻĻā§āϞāĻāĻāĻŋāϰ āĻāĻžāϰā§āϝāĻāϰ āĻĻā§āϰā§āĻā§āϝ āĻāϤ?
āϏāĻŽāĻžāϧāĻžāύ :
L = (gT2)/4Ī2) = {9.8Ã(.9Ã2)2}/(4Ī2) T = .9Ã2s
â´ L = 0.80nm [Answer]
ā§Ŧ. āĻāĻāĻāĻŋ āϏā§āĻā§āύā§āĻĄ āĻĻā§āϞāĻ 21.6s āϧā§āϰ⧠āĻāϞ⧠āĨ¤ āĻāύāĻŋāϰ āĻāĻā§āϰāϤāĻž āύāĻŋāϰā§āĻŖā§ āĻāϰ āĨ¤ [R = 4000mile]
āϏāĻŽāĻžāϧāĻžāύ :
(86400-x)/86400 = â{(R-h)/R} R = 4000mile
â (86400-21.6)/86400 = â{(4000-h)/4000} x = 21.6
â h = 1.999 â 2
â´ h = 2 mile [Answer]