Laplace Transforms: Coupled Springs - Revision history

Jaymin.joseph at 00:34, 11 December 2009

2009-12-11T00:34:56Z

← Older revision		Revision as of 17:34, 10 December 2009
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	'''Part 6: Convolution'''		'''Part 6: Convolution'''

			the definition of convolution of two functions is,

			<math>y(t)=f(t)*h(t)=\int_{-\infty}^{\infty}{f(\tau)h(t-\tau)d\tau}=\int_{\infty}^{-\infty}{f(t-\tau)h(\tau)d\tau}</math>

			applying the definition of convolution to this system we get:

			[[Image:7.jpg]]

Jaymin.joseph at 00:11, 11 December 2009

2009-12-11T00:11:45Z

← Older revision		Revision as of 17:11, 10 December 2009
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	[[Image:5.jpg]]		[[Image:5.jpg]]



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	[[Image:6.jpg]]		[[Image:6.jpg]]

			'''Part 4: Bode Plot'''



			'''Part 5:Magnitude Frequency Response '''




			'''Part 6: Convolution'''

Jaymin.joseph at 23:06, 10 December 2009

2009-12-10T23:06:41Z

← Older revision		Revision as of 16:06, 10 December 2009
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	'''Part 2: Inverse Laplace Transform'''		'''Part 2: Inverse Laplace Transform'''

			[[Image:5.jpg]]


			'''Part 3: Initial-Value & Final-Value Theorem'''

			By definition, the Initial-Value Theorem is,

			<math>\lim_{s\rightarrow \infty} sX(s)=x(0)\,</math>

			and the Final-Value Theorem is,

			<math>\lim_{s\rightarrow 0} sX(s)=x(\infty)\,</math>


			Applying this to the system i get the following.

			[[Image:6.jpg]]

Jaymin.joseph at 22:36, 10 December 2009

2009-12-10T22:36:25Z

← Older revision		Revision as of 15:36, 10 December 2009
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			'''Jaymin Joseph'''

	'''Part 1: Laplace Transform'''		'''Part 1: Laplace Transform'''

Jaymin.joseph: New page: '''Part 1: Laplace Transform''' '''Problem Statement:''' (Equations typed out in mathcad and uploaded as images) This is a system of two masses connected by two springs with spring cons...

2009-12-10T22:36:04Z

New page: '''Part 1: Laplace Transform''' '''Problem Statement:''' (Equations typed out in mathcad and uploaded as images) This is a system of two masses connected by two springs with spring cons...

New page

'''Part 1: Laplace Transform'''

'''Problem Statement:'''
(Equations typed out in mathcad and uploaded as images)

This is a system of two masses connected by two springs with spring constants k1 and k2.
This system is shown below.
[[Image:fbd.JPG]]

From the FBD, the equations of motion can be determined to be as follows:

[[Image:2.jpg]]

To solve the system let K1=6 k2=4, m1=1, m2=1 and x1(0)=0, x1'(0)=1 x2(0)=0, x2'(0)=-2

[[Image:3.jpg]]

[[Image:4.jpg]]

'''Part 2: Inverse Laplace Transform'''