Find Ordinary differential equation, Laplace, Transfer function 、k, spring constant , imasS (0 Xo and χ 5 kg, k =...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is attached to a m > 0 gram block. The spring starts from rest (x(0) - x'(0) 0 and is periodically forced with force f(t) - A sin(wft), with amplitude A > 0. (a) Write down the differential equation describing the displacement of the spring and the initial condition. (b) Solve the initial value problem from (a) using the Laplace transform. (c) What happens to the solution...
a) Find the transfer function. (k: spring coefficient)
b) Using inverse Laplace transform find displacement (x)
m
(1 point) Consider the ordinary differential equation d2G 05 - G = 8(x – xo) on - < x < 0 dr2 where 8 is the delta function. Find the continuous solution G = G(x) such that limz+- G(x) = 0 and limz-40 G(x) = 0. The function u = G(x) is given by G= G for – 0 < x < XO, G = for Xo < x < 0. In your answers, type coas x0.
a) Find the transfer function.
(k: spring coefficient)
b) Using inverse Laplace transform
Find the displacement (x).
Şekil 2. mass-spring system
Consider a CTLTI system described by the following ordinary differential equation with constant coefficients: N M dky(t) 2 ak ak dtk , dkx(t) Ok atk bk - 2 k=0 k=0 The system function H(s) is defined as the Laplace transform of the impulse response h(t) of the system. Write and prove the expression of H(s) as a function of the coefficients of the differential equation. Justify each single step of the proof from first principles (hypothesis, thesis, proof).
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
Laplace transfer functions and ODE?
1) Here is a differential equation. Please find the Laplace
transfer function C(s)/R(s). Note that Initial conditions are
zero.
***answer provided, please show work
ANS:
2) Here is a Laplace transfer function. Please find the
corresponding ODE.
ANS:
dct) 9, ... - 4 20rc and²c(t) , - dt2 CE) 2 dct) dr(t) . - + 20r(t) + 5 - 2- d+3 dt dt² 57년 5월 S P(s) = C(9) = 52+4 R(S) (s*+1) dic tur...
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...
(a) Find the period of oscillation for a spring-mass system where the spring constant (k) is 24 N/m and the mass (m) is 6 kg. (b) Write an equation for x(t) if the spring is stretched to an amplitude of 10 cm from its equilibrium position x = 0 at t = 0. (c) Write an equation for the following initial conditions: at t = 0, the mass is at x = 0 and has a velocity of +3 cm/s.
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...