Problem 5 Exam 1 - Revision history

John.hawkins at 06:11, 5 February 2010

2010-02-05T06:11:17Z

← Older revision		Revision as of 23:11, 4 February 2010
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	==Read By==		==Read By==
			John Hawkins

Brian.Roath at 05:26, 4 February 2010

2010-02-04T05:26:26Z

← Older revision		Revision as of 22:26, 3 February 2010
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	==Author==		==Author==
	Brian Roath		Brian Roath

			==Read By==

Brian.Roath at 05:24, 4 February 2010

2010-02-04T05:24:13Z

← Older revision		Revision as of 22:24, 3 February 2010
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	Find the transfer function of the shock absorber and create the Bode plot of it.		Find the transfer function of the shock absorber and create the Bode plot of it.

	~~<insert drawn image of~~ shock absorber>		[[Image:SD_FBD.jpg\|thumb\|800px\|right\|The shock absorber in its uncompressed state and compressed state.]]

	~~<insert drawn image of FBD>~~
	==Equations==		==Equations==

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	<math> H(s) = \frac {\frac {1} {1000}} {s^2 + 2s + 400} \ </math> <br> <br>		<math> H(s) = \frac {\frac {1} {1000}} {s^2 + 2s + 400} \ </math> <br> <br>

	This final transfer function ~~and~~ the MATLAB-~~generated~~ figure ~~at right~~ are the final solutions.		This final transfer function generates the MATLAB-created figure below are the final solutions.

	[[Image:Bode_Plot_2.JPG\|thumb\|560px\|~~right~~\|The Bode plot of the transfer function.]] <br \> <br>		[[Image:Bode_Plot_2.JPG\|thumb\|560px\|center\|The Bode plot of the transfer function.]] <br \> <br>

	==Author==		==Author==
	Brian Roath		Brian Roath

Brian.Roath: /* Equations */

2010-02-04T02:37:33Z

Equations

← Older revision		Revision as of 19:37, 3 February 2010
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	This final transfer function and the MATLAB-generated figure at right are the final solutions.		This final transfer function and the MATLAB-generated figure at right are the final solutions.

	[[Image:Bode_Plot_2.JPG\|thumb\|560px\|The Bode plot of the transfer function.~~\|right~~]] <br> <br>		[[Image:Bode_Plot_2.JPG\|thumb\|560px\|right\|The Bode plot of the transfer function.]] <br \> <br>

	==Author==		==Author==
	Brian Roath		Brian Roath

Brian.Roath at 02:34, 4 February 2010

2010-02-04T02:34:12Z

← Older revision		Revision as of 19:34, 3 February 2010
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	==Designed Problem Statement==		==Designed Problem Statement==

	A car of mass (m) 1000 kg rests on a shock absorber that has a damper coefficient (<math> \beta </math>) of 2,000 N<math>\cdot</math>s/m and a spring coefficient (k) of 400,000 N/m. A tree lands on the car, delivering a force of <math>f_t</math> to the car and consequently the shock absorber.		A car of mass (<math> m \ </math>) 1000 kg rests on a shock absorber that has a damper coefficient (<math> \beta \ </math>) of 2,000 N<math>\cdot</math>s/m and a spring coefficient (<math> k \ </math>) of 400,000 N/m. A tree lands on the car, delivering a force of <math>f_t</math> to the car and consequently the shock absorber.

	Find the transfer function of the shock absorber and create the Bode plot of it.		Find the transfer function of the shock absorber and create the Bode plot of it.
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	We can now plug it into the transfer function equation, which is written as: <br>		We can now plug it into the transfer function equation, which is written as: <br>
	<math> H(s) = \frac {Y(s)} {F(s)} \ </math> The input function is <math> F(s) \ </math>, which is the Laplaced version of <math> f(t) \ </math>, because it includes the force of the tree falling on the car, which is the factor that disturbs the system.		<math> H(s) = \frac {Y(s)} {F(s)} \ </math> The input function is <math> F(s) \ </math>, which is the Laplaced version of <math> f(t) \ </math>, because it includes the force of the tree falling on the car, which is the factor that disturbs the system. <br> <br>

	[[Image:Bode_Plot_2.JPG\|thumb\|560px\|The Bode plot of the transfer function.\|right]]		Plugging in our output function into the transfer function equation, we get the following: <br>
			<math> H(s) = \frac {\frac {\frac {F(s)} {m}} {s^2 + \frac {\beta s} {m} + \frac {k} {m}}} {F(s)} \ </math> <br> <br>

			This can simplify to: <br>
			<math> H(s) = \frac {\frac {1} {m}} {s^2 + \frac {\beta s} {m} + \frac {k} {m}} \ </math> <br> <br>

			Plugging in the given values for <math> m \ </math>, <math> \beta \ </math>, and <math> k \ </math>, the simplified transfer function becomes: <br>
			<math> H(s) = \frac {\frac {1} {1000}} {s^2 + \frac {2000s} {1000} + \frac {400000} {1000}} \ </math> <br> <br>
			<math> H(s) = \frac {\frac {1} {1000}} {s^2 + 2s + 400} \ </math> <br> <br>

			This final transfer function and the MATLAB-generated figure at right are the final solutions.

			[[Image:Bode_Plot_2.JPG\|thumb\|560px\|The Bode plot of the transfer function.\|right]] <br> <br>

	==Author==		==Author==
	Brian Roath		Brian Roath

Brian.Roath: /* Equations */

2010-02-04T02:03:20Z

Equations

← Older revision		Revision as of 19:03, 3 February 2010
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	<insert drawn image of FBD>		<insert drawn image of FBD>
	=Equations=		==Equations==

	The force of the tree and the force of the car's weight due to gravity can be combined into one equation. <br>		The force of the tree and the force of the car's weight due to gravity can be combined into one equation. <br>

Brian.Roath: /* General Problem Statement */

2010-02-04T02:02:58Z

General Problem Statement

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 Set up and solve a simple spring mass problem that models a car's shock absorber system.
 ==Author==
 Brian Roath

Brian.Roath at 01:08, 3 February 2010

2010-02-03T01:08:23Z

← Older revision		Revision as of 18:08, 2 February 2010
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	==General Problem Statement==		==General Problem Statement==
	Set up and solve a simple spring mass problem that models a car's shock absorber system.		Set up and solve a simple spring mass problem that models a car's shock absorber system.


			==Author==
			Brian Roath

Brian.Roath: New page: ==General Problem Statement== Set up and solve a simple spring mass problem that models a car's shock absorber system.

2010-02-03T01:07:31Z

New page: ==General Problem Statement== Set up and solve a simple spring mass problem that models a car's shock absorber system.

New page

==General Problem Statement==
Set up and solve a simple spring mass problem that models a car's shock absorber system.