Given: Mass = M, Radius = R, Moment of Inertia = I, Distance =  H, Gravity = g, Initial timing = 0 Unknown =  How long will the [delta t] process take? (time) Please keep in mind that almost every variable is unknown! We are given no numbers and are instructed to generate a solution using the variables [ "R, M, g, I and H." ]  Target =  Find an equation that, if we could substitute numbers, would determine how long the process would take.  Newton's second law and torque seem to be relevant based on how the problem is written. * Also please show drawing based on what we are calculating

Context The needle of a sewing machine makes a repetitive up and down motion which is described by the equation y(t)=Acos(wt) To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in ? of the needle as a function of time. Constraints and information The parameter A represents the range of motion (in m);The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second;The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem;Modelization Establish the model for the y velocity of the needle as a function of time and the parameters A and w. Then test your model by calculating the speed in y of the needle at the moment and with the given parameters: Moment: 4.1 s Amplitude: 0.012 m Angular frequency: 17.9 rad/s

Q: for the following equation, what are the units of x., u, and a if X, is the distance in m. t, is the time in second? [X. x3 = + u?t +

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I want to run several shocks in my calibrated DSGE model. I want the shock “a” to happen at period 0, shock “b” at period 2 and shock “c” at period 5. Also, I want to run a shock of 1 % to the variable “a”, 2 % to variable “b” and 10 % to variable “c”. How would I write it in the Dynare code? The model is log-linearized around the steady state and all endogenous variables are set at 0 at the steady state.

Q2/ For the system shown below, use Newton's method to find the system matrix [M],and [K]

The equation of motion of a simplified model mechanical system is given below. of a [ ]] [] [] [] m₂ O m₂ m₁ = 40 kg m m / m₂ = 130 kg, k₁ = 20,000~ k₂ = 10,000 N a) Natural freequency 2 b) Find the mass normalized mode shapes of the system. C) Draw the mass normalized mode shapes.

- Python 3 (pyke We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P= x0, x1,x2,..., Xn,...,xN. Each interval is Ax = (b-a)/N. $ The equation for the Simpson numerical integration rule is derived as: df(xn)) + 2 (Σ=2n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change). Sof(x)dx≈ [f(x) + 4 (N= []: 'Complete the function given the variables N, a,b and return the value as "TotalArea". " "Don't change the predefined content only fill your code in the region 'YOUR CODE" a Idle Mem: 262.63/12288.00 MB F4 R from math…

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