Problem 2 (20 points total): 4 Consider the following system for Parts a-c. 2 N-s/m x2(t)...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
please answer all parts.
4.30 In the SMD system shown in Fig. P4.30, vx(t) is the input velocity of the platform and vy(t) is the output velocity of the 100 kg mass. v(t) 100 kg Ns 100 100 S 100 kg 100 N Sv() 100 Figure P4.30: SMD system of Problem 4.30. APPLICATIONS OF THE LAPLACE TRANSFORM PTER 4 (a) Draw the equivalent s-domain circuit. (c) Determine the frequency response. Hint: Use two node equations.
4.30 In the SMD system...
please answer all parts.
4.30 In the SMD system shown in Fig. P4.30, vx(t) is the input velocity of the platform and vy(t) is the output velocity of the 100 kg mass. v(t) 100 kg Ns 100 100 S 100 kg 100 N Sv() 100 Figure P4.30: SMD system of Problem 4.30. APPLICATIONS OF THE LAPLACE TRANSFORM PTER 4 (a) Draw the equivalent s-domain circuit. (c) Determine the frequency response. Hint: Use two node equations.
Problem#3 (16 points) Consider a system that has R(S) as the input and Y (S) as the output. The transfer function is given by: Y(S) R(S) 45+12 What are the poles of the system? For r(t) output in the time-domain y(t) For r(t) = t, t output in the time-domain y(t) 1- 2- 1,t 0, use partial fraction expansion and inverse Laplace transform to find the 3- 0, use partial fraction expansion and inverse Laplace transform to find the
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_ M2 4 kg fv2 4 N-s/m fv= 4 N-s/m (a) fit) Frictionless N/m -xj(t) O000 16 N-s/m 15 N/m 0000 4 N-s/m M1 8 kg M2-3 kg Frictionless Frictionless (b)
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_...
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0) = 0, where g(t) = if 9 t<oo. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y() by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below) ! help (formulas) b. Solve your equation for...
part a and b only first paragraph already done (theta)
Problem 3.35 (6 points) Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kgP and radius 0.05 m, as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equations of motion in terms of angular displacement θ of the rod and displacement-V,ofthe wheel center Assume the wheel does not slip. Linearize...
Verify the following using MATLAB
2) (a) Consider the following function f(t)=e"" sinwt u (t (1) .... Write the formula for Laplace transform. L[f)]=F(6) F(6))e"d Where f(t is the function in time domain. F(s) is the function in frequency domain Apply Laplace transform to equation 1. Le sin cot u()]F(s) Consider, f() sin wtu(t). From the frequency shifting theorem, L(e"f()F(s+a) (2) Apply Laplace transform to f(t). F,(s)sin ot u (t)e" "dt Define the step function, u(t u(t)= 1 fort >0...
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'(0)=x(0)=0 Find the solution of this differential equation using Laplace transforms. F(t) 7m
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...