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Unformatted text preview: lVIECH 310 Second Hourly Examination 1
16 Apr 04 ' CLOSED BOOK AND NOTES NAlVHE 1. [25 pts] A SOO—kg cannon propels a 5kg cannonball at a
speed of 500 m/sec. Of course this causes the
gun barrel to recoil. A springdamper recoil
mechanism is used to bring the barrel to rest in
the SHORTEST POSSIBLE TIME WITHOUT
OSCILLATIN G. In practice this time is 1
second. ‘ Solve for the barrel recoil deﬂection, x(t), sketch the result, and ﬁnd the maximum
deﬂection. Suppose that the damper is removed. Now What is the maximum deﬂection? Page 2 of 4 pages
2. [30 pts] A volume plethysmograph allows us to moni
tor pressure changes in a sealed room. A
pneumatic bellows with area A = 1 measures F
= PA by distending viscoelastically. A pen
With mass M = 1 records pressure on a moving
strip chart. K and b are tuned to produce the
fastest possible settling time. a) From the data, ﬁnd K, b, and the pressure
p(t) which produced this outburst. (20 pts). b) Obviously the response curve doesn’t reproduce the signal very well. Make a sim
ple adjustment of the pen to improve this instrumentation, and plot the result. (10 pts) Page 3 of 4 pages
3. [30 pts] The diagram models a juggler balancing a
pole (mass mp) on her nose. By moving her
head (mass M) she can correct any tendency
for the pole to ﬂop over. This is accomplished
by supplying a force M to her head by neck
muscles (not shown). This makes a nice 410
project, except that ﬁrst we have to ﬁnd the
transfer function. a) Find the dynamics equations, making smallangle approximations. b) Too bad! Even with the small—angle approximations the dynamics equations are
' equations are still nonlinear. But you do see how to eliminate X(t) — and then
you can program SIMULINK to calculate 6(t). Assume that F is 00541;. Page 4 of 4 pages 4. [15 pts] SPOT CHECKS  5 pts each a) Find the % OS AND the ﬁnal value when a unit step force
acts on this system. b Use SIMULINK to generate the function f(t) = 6+4)“2 0) Given M + bill—)5: + KX = F(t) . Suppose F(t) is tripled; then the system time constant (circle one) 1) increases 2) decreases 3) stays the same 4) may increase or decrease,
depending on M, h, K and F(t) I; {fa2 gwﬁs + wig £7 a é/m é am 65 ﬁg
12% a; a PM?$ 3:3 Egg. aw = 2a iﬁw FEM)!
@meémwﬁ Wﬁamz xébmﬂa E56» £ was é‘é‘éﬁ; 515:. 5”} ...
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 Spring '09
 Snyder
 pts, Cannon, shortest possible time, barrel recoil deﬂection, possible settling time, tor pressure changes

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