- A
steel cable has diameter 1 cm and length 20 m. What is its spring constant? What would be the frequency of
vertical oscillations of 5000 kg mass that was hung on this cable?
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- In
the above problem, what would be the frequency of horizontal (i.e.
pendulum) oscillations?
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- When
four 200 lb men get into a 3000 lb car it lowers by 1.5”. Determine the frequency at which this
car will oscillate up and down.
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- What
is the period of a pendulum that is 10 cm long?
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- Is
it surprising that the period of a pendulum is independent of its
mass? Why or why not?
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- Estimate
the amplitude a pendulum must reach before the “small swing” assumptions
start breaking down.
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- Originally
the meter was proposed as being the length of a pendulum whose period
was one second, or whose half-period
was one second. This would create
a nice, portable standard of measurement that anyone with a rock and a
piece of string could have created.
Thomas Jefferson
pushed for this, and Congress was up for it. Alas, in one of the greatest triumphs of bureaucracy
known to history, scientists chose to base the meter on the size of
the Earth instead. That meant the
meter was a size that no one but scientists understood – but it created
a lot of government jobs for scientists at the time. Congress scratched its head, and we
measure in feet and yards.
What are the lengths of the two pendulums described above? Give your answers in cm and inches.
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- PHY 232 Only -- If x = A
sin(wt
+ f),
derive an equation for the KE and PE in a SHO. Show that KE + PE = E is a
constant. Make a graph of KE, PE,
and E, putting all three plots on one set of axes.
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- PHY 232 Only -- Show
that the equation
x = A sin (wt)
+ B cos(wt)
also solves the differential equation for a SHO.
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