Yahoo Answers: Answers and Comments for A mass m = 5.0 kg is attached to a vertical spring with k = 188 N/m and is set into motion.? [Physics]
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Mon, 07 Dec 2009 01:42:46 +0000
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Yahoo Answers: Answers and Comments for A mass m = 5.0 kg is attached to a vertical spring with k = 188 N/m and is set into motion.? [Physics]
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https://answers.yahoo.com/question/index?qid=20091207014246AAqnYhr
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From Pearlsawme: a)
ω = √ k/m = √ 188/ 5 = 37.6 rad /s. = 2 π ...
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https://answers.yahoo.com/question/index?qid=20091207014246AAqnYhr
Mon, 07 Dec 2009 12:14:47 +0000
a)
ω = √ k/m = √ 188/ 5 = 37.6 rad /s. = 2 π N where N is the frequency
N = 37.6 / 2 π Hz = 5.98 Hz.

b)
Maximum velocity = A ω where A is the amplitude.
Maximum velocity = 0.032*37.6 = 1.2032 m/s

c)
y2 = A sin ωt2 and y1 = A sin ωt1.
sin ωt1 = y1/ A= 1.5 / 3.2 = 0.46875
ωt1 = 0.4879
t1 =0.4879 / 37.6 = 0.013 s.
sin ωt2 = y2/ A= 2.5 / 3.2 = 0.78125
ωt2 = 0.8967
t2 = 0.8967/ 37.6 = 0.024 s
The time difference = 0.024 0.013 = 0.011 s

d)
The max k.e = 1/2 m [ A ω] ^2 is a constant.
that is Aω is a constant.
A1 ω1 = A2 ω2
ω2/ ω1 = A1/A2
ω2/ ω1 = √ k2/k1= A1/A2
Given k2 = 2k1
√ k2/k1 = √2 = A1/A2
Hence A2 = A1 / √2
The factor is 1/√2 = 70.71%
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From Joe: (a) f = k/m = 188/5 = 37.6 Hz
(b) x(t) = As...
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https://answers.yahoo.com/question/index?qid=20091207014246AAqnYhr
Mon, 07 Dec 2009 10:02:02 +0000
(a) f = k/m = 188/5 = 37.6 Hz
(b) x(t) = Asin(f*t) = 3.2sin(37.6t)
v(t) = d/dt(x(t)) = 129.32*cos(37.6t)
cosine maximum = 1, at t = 0 (assuming dampened harmonic oscillator equation):
v(max) = 1.2932 (m/s)
(c) no idea
(d) use eq. in (b) for damp harmonic osc.
(e) no idea