3. [10 pts) Consider a familiar horizontal ideal spring-mass system. The solutions for both the velocity...
NOTE:Follow the Runge-Kutta Method.Any programming
language(Matlab) can be used.Plot Position-Time and Velocity-Time
graphs.
The spring-mass system is at rest when the force P(t) is applied, where P(t) = 100 N 20 N when t < 2 s when t>2 s The differential equation for the ensuing motion is P(t) k mm Determine the maximum displacement of the mass. Use m= 2.5 kg and k= 75 N/m.
a can be skipped
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): 2x + 2x + x=u, x(0) = 0, *(0) = 0 where u is the Unit Step Function (of magnitude 1). a. Use MATLAB to obtain an analytical solution x(t) for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for x(t). Also obtain a plot of .x(t) (for a simulation of 14 seconds)...
Consider the Spring-Mass-Damper system: 17 →xt) linn M A Falt) Ffl v) Consider the following system parameter values: Case 1: m= 7 kg; b = 1 Nsec/m; Fa = 3N; k = 2 N/m; x(0) = 4 m;x_dot(0)=0 m/s Case2:m=30kg;b=1Nsec/m; Fa=3N; k=2N/m;x(0)=2m;x_dot(0)=0m/s Use MATLAB in order to do the following: 1. Solve the system equations numerically (using the ODE45 function). 2. For the two cases, plot the Position x(t) of the mass, on the same graph (include proper titles, axis...
Thanks in advance
4. (8 points) We consider the mass-spring-dnmper systen in Figure &: A block af mes is saspended fron the eeiling by n spring with eonistant k nnd unstretched length lo and a damper with damping eoeficient d The block ean anly move vertienlly nnd its poesition is theresore fually deseribed by the z-courdinnte. An nlternative poeition is mensued from the statie rest position Furthermore, ngravitational neeclerstioa with mngnitude g is present. SYSTEM Fgure & A rigid body...