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 Post subject: SHM
PostPosted: Fri, 31 Oct 2003 00:57:01 UTC 
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Location: Edmonton, Canada.
1) A computer to be used in a satellite must be able to withstand accelerations up to 25 times the acceleration due to gravity. In a test to see whether it meets this specification, the computer is bolted to a frame that is vibrated back and forth in simple harmonic motion at a frequency of 9.5 Hz. What is the minimum amplitude of vibration that must be used in this test?

2) A pendulum clock can be approximated as a simple pendulum of length 1.00 m and keeps accurate time at a location where g is 9.83 m/s2. In a location where g is 9.78 m/s2, what must be the new length of the pendulum, such that the clock continues to keep accurate time (that is, its period remains the same)?

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PostPosted: Fri, 31 Oct 2003 04:00:09 UTC 
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Joined: Sun, 22 Jun 2003 18:00:06 UTC
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1. w = 2pi*f

since a(t) = -Aw^2*cos(wt), the max amplitude of acceleration will occur when cos(wt) = -1 or 1

|a(t)| = Aw^2
|a(t)|/w^2 = A
25g/(2pi*f)^2 = A
Amplitude = approx .07 m

2. T = 2pi*sqrt(L/g)

2pi*sqrt(1/9.83) = 2pi*sqrt(L/9.78)
1/9.83 = L/9.78
L = 9.78/9.83 = approx 0.995 m


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