Laplace transforms: Critically Damped Spring Mass system - Revision history

Gregory.peterson: /* Break Points____ */

2009-12-10T21:26:07Z

______________________________Break Points__________________________________

← Older revision		Revision as of 14:26, 10 December 2009
Line 115:		Line 115:


	==~~______________________________Break Points__________________________________~~==		==Break Points==

	<math>\text {Find the Break points using the transfer function.}\,</math>		<math>\text {Find the Break points using the transfer function.}\,</math>

Gregory.peterson: /* State Space */

2009-12-03T06:31:52Z

State Space

← Older revision		Revision as of 23:31, 2 December 2009
Line 167:		Line 167:
	<math>\text {First we need to add an applied force so u(t)=2N }\,</math>		<math>\text {First we need to add an applied force so u(t)=2N }\,</math>

	<math>m=\frac{98.1}{9.81}=~~\frac1~~ 10 kg</math>		<math>m=\frac{98.1}{9.81}=10 kg</math>

	<math>\text {k=40}\,</math>		<math>\text {k=40}\,</math>

Gregory.peterson: /* State Space */

2009-12-03T06:31:35Z

State Space

← Older revision		Revision as of 23:31, 2 December 2009
Line 167:		Line 167:
	<math>\text {First we need to add an applied force so u(t)=2N }\,</math>		<math>\text {First we need to add an applied force so u(t)=2N }\,</math>

	<math>m=\frac{8}{32}=\frac1 ~~4 slugs~~</math>		<math>m=\frac{98.1}{9.81}=\frac1 10 kg</math>

	<math>\text {k=40}\,</math>		<math>\text {k=40}\,</math>

Gregory.peterson: /* State Space */

2009-12-03T06:30:43Z

State Space

← Older revision		Revision as of 23:30, 2 December 2009
Line 169:		Line 169:
	<math>m=\frac{8}{32}=\frac1 4 slugs</math>		<math>m=\frac{8}{32}=\frac1 4 slugs</math>

	<math>\text {k=4}\,</math>		<math>\text {k=40}\,</math>

	<math>\text {C=2}\,</math>		<math>\text {C=40}\,</math>

	<math>\text {x(0)=0}\,</math>		<math>\text {x(0)=0}\,</math>

	<math>\dot{x}(0)=-3</math>		<math>\dot{x}(0)=-4</math>

	<math>\ddot{x}(0)=0</math>		<math>\ddot{x}(0)=0</math>

Gregory.peterson: /* Convolution */

2009-12-03T06:27:27Z

Convolution

← Older revision		Revision as of 23:27, 2 December 2009
Line 160:		Line 160:

	<math>\text {Not exactly the same but remember initial conditions arnt used}\,</math>		<math>\text {Not exactly the same but remember initial conditions arnt used}\,</math>

			==State Space==

			<math>\text {Using state equatons is just another way to solve a system modeled by an ODE }\,</math>

			<math>\text {First we need to add an applied force so u(t)=2N }\,</math>

			<math>m=\frac{8}{32}=\frac1 4 slugs</math>

			<math>\text {k=4}\,</math>

			<math>\text {C=2}\,</math>

			<math>\text {x(0)=0}\,</math>

			<math>\dot{x}(0)=-3</math>

			<math>\ddot{x}(0)=0</math>


			<math>\begin{bmatrix} \dot{x} \\ \ddot{x} \end{bmatrix}=\begin{bmatrix} 0 & 1 \\ -k/m & -C/m \end{bmatrix} \begin{bmatrix} x \\ \dot{x} \end{bmatrix} + \begin{bmatrix} 0 \\ 1/m \end{bmatrix}u(t)</math>

Gregory.peterson: /* Convolution */

2009-12-03T06:21:54Z

Convolution

@@ Line 131: / Line 131: @@
 ==Convolution==
-coming soon...?
+<math>\text {The convolution equation is as follows:  }\,</math>
 Created by Greg Peterson
 Checked by Mark Bernet

Gregory.peterson at 23:07, 27 October 2009

2009-10-27T23:07:55Z

← Older revision		Revision as of 16:07, 27 October 2009
Line 115:		Line 115:


	==~~Break Points~~ ==		==______________________________Break Points__________________________________==

	<math>\text {Find the Break points using the transfer function.}\,</math>		<math>\text {Find the Break points using the transfer function.}\,</math>

Gregory.peterson: /* Given */

2009-10-27T23:06:24Z

Given

← Older revision		Revision as of 16:06, 27 October 2009
Line 13:		Line 13:


	<math>m=\frac{98}{9.81}</math>		<math>m=\frac{98}{9.81}kg</math>

	<math>\text {Spring Constant k=40}\,</math>		<math>\text {Spring Constant k=40}N/m\,</math>

	<math>\text {Damping Constant C=40}\,</math>		<math>\text {Damping Constant C=40}\,</math>

Gregory.peterson: /* Applying this to our problem */

2009-10-27T23:05:41Z

Applying this to our problem

← Older revision		Revision as of 16:05, 27 October 2009
Line 82:		Line 82:


	<math>\text {So as you can see the value for the initial position will be 0. Because the infinity in the denominator always makes the function tend toward zero.}\,</math>		<math>\text {So as you can see the value for the initial position will be 0.}\,</math>
			<math>\text {Because the infinity in the denominator always makes the function tend toward zero.}\,</math>

	<math>\text {Which makes sense because the system is initially in equilibrium. }\,</math>		<math>\text {Which makes sense because the system is initially in equilibrium. }\,</math>
Line 94:		Line 95:

	<math>\text {This shows the final value to be}\,</math>		<math>\text {This shows the final value to be}\,</math>
	<math>-\frac{4}{4}ft</math>		<math>-\frac{4}{4}m</math>

	<math>\text {Which appears to mean the system will be right below equilibrium after a long time. }\,</math>		<math>\text {Which appears to mean the system will be right below equilibrium after a long time. }\,</math>

Gregory.peterson at 23:04, 27 October 2009

2009-10-27T23:04:26Z

← Older revision		Revision as of 16:04, 27 October 2009
Line 127:		Line 127:

	<math>\text {The break points are asymtotes at the point -2 which occurs twice in this particular equation}\,</math>		<math>\text {The break points are asymtotes at the point -2 which occurs twice in this particular equation}\,</math>

			==Convolution==

			coming soon...?

	Created by Greg Peterson		Created by Greg Peterson

	Checked by Mark Bernet		Checked by Mark Bernet

Laplace transforms: Critically Damped Spring Mass system - Revision history

Gregory.peterson: /* ______________________________Break Points__________________________________ */

Gregory.peterson: /* State Space */

Gregory.peterson: /* State Space */

Gregory.peterson: /* State Space */

Gregory.peterson: /* Convolution */

Gregory.peterson: /* Convolution */

Gregory.peterson at 23:07, 27 October 2009

Gregory.peterson: /* Given */

Gregory.peterson: /* Applying this to our problem */

Gregory.peterson at 23:04, 27 October 2009

Gregory.peterson: /* Break Points____ */