In mechanical engineering work an error analysis is usually performed with a Kline-McClintock method that propagates the measurement errors or equivalently the uncertainty in variables/parameters through a governing equation so that the final uncertainty may be estimated using the calculus-based error analysis equation. Consider a double pendulum system as shown below. Y Po(xo, yo) T1 Pi(21,31) X mi 12 P2(x2, Y2) Sketch of a double pendulum system Supplied Information: m = (0.372 +0.003) kg (Rectangular distribution) m (1.647 +0.071) kg (Rectangular distribution) T = (0.420+ 0.036) m (Gaussian distribution) y = (0.362 0.009) m (Gaussian distribution) = (-0.8430.73) m s (Gaussian distribution) V = (1.87 +0.143) m s (Triangular distribution) m2 A double pendulum system consists of two balls each of mass mand m that are interconnected to each other by segments of lengths and 72 respectively. Segment is inflexible and connected to an upper ceiling at a point po which has coordinates (xo.yo) in an XY coordinate system, such that the centre-of-mass of the ball of mass m at the other end of segment r is located at point P which has coordinates (x, y), which is also the end of segment 12 which is flexible such that the other end of segment 1 is connected to the ball of mass m centre-of-mass at point p which has coordinates at (x2, y2). For this system the potential energy may be neglected, gravity acts in a downwards direction, and the equation of motion is specified in terms of four degrees-of-freedom, which specifies the overall kinetic energy of the system. HINT: The constraint that T is constant whilst T is not constant may be simplified by considering a translation of the coordinate system. Considering the above specified system for the double pendulum derive a governing equation for the kinetic energy of the overall system and utilize the supplied uncertainty specification to apply the Kline-McClintock method to perform an error analysis in order to calculate the standard uncertainty of the kinetic energy of the system. Include a computer model developed in Scilab/Xcos with full details of the code with any annotations/explanations with associated compilation details as appropriate so that the measurement model may accept user inputs which may be Rectangular distributions, Gaussian distributions or Triangular distributions. From your developed error analysis approximate the 7-dimensional model of the kinetic energy system as a 3-dimensional model by considering the two inputs which contribute most to the uncertainty of the kinetic energy and utilize that to generate a 3-dimensional graph of the kinetic energy and the corresponding contour plot that specifies the variation in the kinetic energy. Additional points may be earned by determining the expanded uncertainty probability density function of the kinetic energy. Document your work in a type written engineering report of not more than 40 pages inclusive of graphs, diagrams and accompanying computer code that is submitted as a single Adobe PDF file. In mechanical engineering work an error analysis is usually performed with a Kline-McClintock method that propagates the measurement errors or equivalently the uncertainty in variables/parameters through a governing equation so that the final uncertainty may be estimated using the calculus-based error analysis equation. Consider a double pendulum system as shown below. Y Po(xo, yo) T1 Pi(21,31) X mi 12 P2(x2, Y2) Sketch of a double pendulum system Supplied Information: m = (0.372 +0.003) kg (Rectangular distribution) m (1.647 + 0.071) kg (Rectangular distribution) T = (0.420 + 0.036) m (Gaussian distribution) y = (0.362 0.009) m (Gaussian distribution) = (-0.843 0.73) m s (Gaussian distribution) V = (1.87 + 0.143) m s (Triangular distribution) m2 A double pendulum system consists of two balls each of mass mand m that are interconnected to each other by segments of lengths and 72 respectively. Segment is inflexible and connected to an upper ceiling at a point po which has coordinates (xo, Yo) in an XY coordinate system, such that the centre-of-mass of the ball of mass m at the other end of segment r is located at point P which has coordinates (x, y), which is also the end of segment 12 which is flexible such that the other end of segment 1 is connected to the ball of mass m centre-of-mass at point p which has coordinates at (x2, y2). For this system the potential energy may be neglected, gravity acts in a downwards direction, and the equation of motion is specified in terms of four degrees-of-freedom, which specifies the overall kinetic energy of the system. HINT: The constraint that T is constant whilst T is not constant may be simplified by considering a translation of the coordinate system. Considering the above specified system for the double pendulum derive a governing equation for the kinetic energy of the overall system and utilize the supplied uncertainty specification to apply the Kline-McClintock method to perform an error analysis in order to calculate the standard uncertainty of the kinetic energy of the system. Include a computer model developed in Scilab/Xcos with full details of the code with any annotations/explanations with associated compilation details as appropriate so that the measurement model may accept user inputs which may be Rectangular distributions, Gaussian distributions or Triangular distributions. From your developed error analysis approximate the 7-dimensional model of the kinetic energy system as a 3-dimensional model by considering the two inputs which contribute most to the uncertainty of the kinetic energy and utilize that to generate a 3-dimensional graph of the kinetic energy and the corresponding contour plot that specifies the variation in the kinetic energy. Additional points may be earned by determining the expanded uncertainty probability density function of the kinetic energy. Document your work in a type written engineering report of not more than 40 pages inclusive of graphs, diagrams and accompanying computer code that is submitted as a single Adobe PDF file.