An m-mass pendulum is connected to a spring with the spring constant k through the massless rope along I as in the picture. x,i k www point y =0 m The spring is then given a deviation of x, so it moves at a speed of x. Assume point y = 0 is parallel to the spring, so that the potential energy of the pendulum negative value. If the pendulum has a deviation of 0, specify: The system motion equation uses the Euler-Lagrange equation.

Pls see the question in the attcahed image and solve  using either Newton’s method or Lagrange Energy method .

Pls hurry up very urgent with explain what is P and Q

Q1: by using simple energy method find the equation of motion and natural frecquancy of the system shown in the fig 3K. www m ir -X 4K₁ 25(marks) n find the

PROBLEM1: Determine the equation of motion of the following systems: 1080 al*k www 0.51 ghiv Vin & Mass Less, Rigid L J Figure 2-Problem 1-2 a3*m

damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…

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1. The differential equations for a suspension system with input displacement (1) are 2+102 + 100z 10w + 100w w + 40w = ż+ 10z + 30u (a) Assume all initial conditions are zero and convert the equations above to Laplace domain (b) Demonstrate that if you solve for W(s) in the first equation and then substitute this expression for W(s) into the 2nd equation, when you solve for Z(s) you get Z(s) = 3000+300s Ls³ +40s² + 300s + 3000] 3 (c) What is the transfer function for this system? U(S)

2.- Determine if the system shown (modulator) is: (1 point) 2.1- Linear 2.2. Invariant in time.

The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…