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MECH310_PracticeTest2

# MECH310_PracticeTest2 - lVIECH 310 Second Hourly...

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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 5-kg cannonball at a speed of 500 m/sec. Of course this causes the gun barrel to recoil. A spring-damper 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 visco-elastically. 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 small-angle approximations. b) Too bad! Even with the small—angle approximations the dynamics equations are ' equations are still non-linear. 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; {fa-2 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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