Andy's Fourier Series Project - Revision history

Andrew.wooley: /* Analysis */

2010-11-02T03:03:14Z

Analysis

← Older revision		Revision as of 20:03, 1 November 2010
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	<math>\begin{align}		<math>\begin{align}
	x(t) &= x(t+T) = a_0 + \sum_{n=1}^\infty a_n \cos(n\omega_0t) + b_n \sin(n\omega_0t)\\		x(t)&= x(t+T) = a_0 + \sum_{n=1}^\infty a_n \cos(n\omega_0t) + b_n \sin(n\omega_0t)\\
	a_0 &= \frac{1}{T}\int_0^T f(t)\, dt\\		a_0 &= \frac{1}{T}\int_0^T f(t)\, dt\\
	a_n &= \frac{2}{T}\int_0^T f(t)\cos(n\omega_0t)\, dt\\		a_n &= \frac{2}{T}\int_0^T f(t)\cos(n\omega_0t)\, dt\\

Andrew.wooley: /* Analysis */

2010-11-02T03:00:41Z

Analysis

← Older revision		Revision as of 20:00, 1 November 2010
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	The equation of motion is to be considered:		The equation of motion is to be considered:

Andrew.wooley: /* Analysis */

2010-11-02T03:00:22Z

Analysis

← Older revision		Revision as of 20:00, 1 November 2010
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	The equation of motion is to be considered:		The equation of motion is to be considered:




	<math>\begin{align}		<math>\begin{align}
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	\end{align}		\end{align}
	</math>		</math>



	Where k = spring constant and that is assumed to be 70560 and the mass = 2500 lbm.		Where k = spring constant and that is assumed to be 70560 and the mass = 2500 lbm.



	<math>\begin{align}		<math>\begin{align}

Andrew.wooley: /* Analysis */

2010-11-02T03:00:02Z

Analysis

← Older revision		Revision as of 20:00, 1 November 2010
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	These are the equations of Fourier Series:		These are the equations of Fourier Series:


	<math>\begin{align}		<math>\begin{align}
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	\end{align}		\end{align}
	</math>		</math>


	The equation of motion is to be considered:		The equation of motion is to be considered:

Andrew.wooley: /* Analysis */

2010-11-02T02:59:45Z

Analysis

← Older revision		Revision as of 19:59, 1 November 2010
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	</math>		</math>

	Where k = spring constant and that is assumed to be 70560.		Where k = spring constant and that is assumed to be 70560 and the mass = 2500 lbm.

	<math>\begin{align}		<math>\begin{align}
	x(t) = c_1 cos((sqrt(k) t)/sqrt(m))+c_2 sin((sqrt(k) t)/sqrt(m))\\		x(t) = c_1 cos\frac{sqrt(k) t)}{sqrt(m)}+c_2 sin\frac{sqrt(k) t}{sqrt(m)}\\
	\end{align}		\end{align}
	</math>		</math>

Andrew.wooley: /* Analysis */

2010-11-02T02:54:08Z

Analysis

← Older revision		Revision as of 19:54, 1 November 2010
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	==Analysis==		==Analysis==


			These are the equations of Fourier Series:


			<math>\begin{align}
			x(t) &= x(t+T) = a_0 + \sum_{n=1}^\infty a_n \cos(n\omega_0t) + b_n \sin(n\omega_0t)\\
			a_0 &= \frac{1}{T}\int_0^T f(t)\, dt\\
			a_n &= \frac{2}{T}\int_0^T f(t)\cos(n\omega_0t)\, dt\\
			b_n &= \frac{2}{T}\int_0^T f(t)\sin(n\omega_0t)\, dt\\
			\end{align}
			</math>


	The equation of motion is to be considered:		The equation of motion is to be considered:

	<math>m x''(t)+k x(t) = 0</math>		<math>\begin{align}
			m x''(t)+k x(t) = 0\\
			\end{align}
			</math>

	Where k = spring constant and that is assumed to be .		Where k = spring constant and that is assumed to be 70560.

	<math>x(t) = c_1 cos((sqrt(k) t)/sqrt(m))+c_2 sin((sqrt(k) t)/sqrt(m))		<math>\begin{align}
			x(t) = c_1 cos((sqrt(k) t)/sqrt(m))+c_2 sin((sqrt(k) t)/sqrt(m))\\
			\end{align}
	</math>		</math>

Andrew.wooley: /* Project Statement */

2010-11-02T02:44:05Z

Project Statement

← Older revision		Revision as of 19:44, 1 November 2010
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	==Damped Spring Mass With Dash Pot==		==Damped Spring Mass With Dash Pot==
	==Project Statement==		==Project Statement==
	I chose to analyze a car's suspension. Only one wheel's system will be considered to simplify calculations. The car will be simulated as running over a constant road surface similar to that of an ideal driving surface. The Fourier series can be represented with proper assumptions.		I chose to analyze a car's suspension. Only one wheel's system will be considered to simplify calculations. The car will be simulated as running over a constant road surface similar to that of an ideal driving surface. The Fourier series can be represented with proper assumptions. A coil spring will be considered.

	First a picture to represent the system used in a car.		First a picture to represent the system used in a car.

Andrew.wooley: /* Analysis */

2010-11-02T02:43:36Z

Analysis

← Older revision		Revision as of 19:43, 1 November 2010
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	==Analysis==		==Analysis==
	The equation of motion is to be considered:		The equation of motion is to be considered:

			<math>m x''(t)+k x(t) = 0</math>

			Where k = spring constant and that is assumed to be .

			<math>x(t) = c_1 cos((sqrt(k) t)/sqrt(m))+c_2 sin((sqrt(k) t)/sqrt(m))
			</math>

Andrew.wooley: /* Project Statement */

2010-11-02T02:24:56Z

Project Statement

← Older revision		Revision as of 19:24, 1 November 2010
Line 1:		Line 1:
	==Damped Spring Mass With Dash Pot==		==Damped Spring Mass With Dash Pot==
	==Project Statement==		==Project Statement==
	I chose to analyze a car's suspension. Only one wheel's system will be considered to simplify calculations. The car will be simulated as running over a constant ~~uneven~~ road surface similar to that of ~~a dirt road or rough country road~~. The Fourier series can be represented with proper assumptions.		I chose to analyze a car's suspension. Only one wheel's system will be considered to simplify calculations. The car will be simulated as running over a constant road surface similar to that of an ideal driving surface. The Fourier series can be represented with proper assumptions.

	First a picture to represent the system used in a car.		First a picture to represent the system used in a car.
Line 13:		Line 13:


	To imagine this system accurately we must flip the diagram upside-down and the ground can then be the road and the mass (M) and the force of the car (f) can be in the proper direction. To find the Fourier series the Dash pot (D) will be neglected. The Dash pot will be implemented later to show the effectiveness of the car's suspension to slow the wave motion caused by ~~rough~~ surfaces.		To imagine this system accurately we must flip the diagram upside-down and the ground can then be the road and the mass (M) and the force of the car (f) can be in the proper direction. To find the Fourier series the Dash pot (D) will be neglected. The Dash pot will be implemented later to show the effectiveness of the car's suspension to slow the wave motion caused by road surfaces.

	==Analysis==		==Analysis==
	The equation of motion is to be considered:		The equation of motion is to be considered:

Andrew.wooley: /* Project Statement */

2010-11-02T02:23:32Z

Project Statement

← Older revision		Revision as of 19:23, 1 November 2010
Line 1:		Line 1:
	==Damped Spring Mass With Dash Pot==		==Damped Spring Mass With Dash Pot==
	==Project Statement==		==Project Statement==
	I chose to analyze a car's suspension. Only one wheel's ~~systems~~ will be considered to simplify calculations. The car will be simulated as running over a constant uneven road surface similar to that of a dirt road or rough country road. The Fourier series can be represented with proper assumptions.		I chose to analyze a car's suspension. Only one wheel's system will be considered to simplify calculations. The car will be simulated as running over a constant uneven road surface similar to that of a dirt road or rough country road. The Fourier series can be represented with proper assumptions.

	First a picture to represent the system used in a car.		First a picture to represent the system used in a car.
Line 14:		Line 14:

	To imagine this system accurately we must flip the diagram upside-down and the ground can then be the road and the mass (M) and the force of the car (f) can be in the proper direction. To find the Fourier series the Dash pot (D) will be neglected. The Dash pot will be implemented later to show the effectiveness of the car's suspension to slow the wave motion caused by rough surfaces.		To imagine this system accurately we must flip the diagram upside-down and the ground can then be the road and the mass (M) and the force of the car (f) can be in the proper direction. To find the Fourier series the Dash pot (D) will be neglected. The Dash pot will be implemented later to show the effectiveness of the car's suspension to slow the wave motion caused by rough surfaces.








	==Analysis==		==Analysis==
	The equation of motion is to be considered:		The equation of motion is to be considered: