A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
Suppose a mass of 1 kg is attached to a spring with spring constant k = 2, and rests at equilibrium position. Starting at t = 0, an external force of f(t) = e t is applied to the system. Suppose the surrounding medium offers a damping force numerically equal to β times the instantaneous velocity, where β > 0 is some given number. (a) What is the IVP governing this harmonic motion. (b) For what value(s) of β will...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
A į kg mass is attached to a spring with stiffness 4N/m and a damping constant 1 N sec/m. The mass is displaced im to the left and given a velocity of 1m/sec to the left. (i) Find the equation of motion of the mass. (ii) What kind of motion do you get? Underdamped, overdamped or critically damped? (iii) What is the maximum displacement that the mass will attain?
plz print your result -1 points МУ Not A mass weighing 3V 10 N stretches a spring 2 m. The mass is attached to a dashpot device that offers a damping force numerically equal to β (B > 0) times the instantaneous velocity Determine the values of the damping constant B so that the subsequent motion is overdamped, critically damped, and underdamped. (If an answer is an interval, use interval notation. Use g 9.8 m/s2 for the acceleration due to...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
Math 216 Homework WebHWI, PIUUIUM A mass with mass 7 is attached to a spring with spring constant 42 and a dashpot giving a damping 55. The mass is set in motion with initial position 6 and initial velocity 8. (All values are given in consistent units) Find the position function (t) = The motion is (select the correct description) A. underdamped B. overdamped C. critically damped 0 ). Finally find the undamped position function u(t) = Cocos(wist - 00)...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
Solve it with matlab 25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...