The equation of motion of a system is derived as : 2 d 2 x d t 2 + 40 d x d t + 1800 x = 120 sin 15 t. Its magnification factor is
Structural Dynamics (12 points) For the system shown below, 1. Determine A) The equation of motion. B) The maximum steady state force in the damper. C) The maximum steady state absolute acceleration. D) The maximum steady state force in the spring. Given: x(t)-2" sin(3.2t) W= 5000 lbs. K 1,863.4 lb/in C- 5 lb-s/in Ct) (12 points) For the system shown below, 1. Determine A) The equation of motion. B) The maximum steady state force in the damper. C) The maximum...
For the system shown below, find a) the modeling equation in x; b) natural frequency; c) damping ratio; d) frequency ratio; e) Magnification factor and f) Steady-state amplitude. M, sin or m = 10 kg 1 = 0.1 kg-m = 10 cm k = 1.6 x 10 **640 N. M = 2 zie " * = 180 rad
2. The equation of motion for a mass of 100g in a mass-spring system is 27t. X(t) = 3Cos() Find the value of spring constant k.
Determine the equation of motion and calculate the natural frequency of the system when x(t), the downward displacement of the block, is measured from the system's equilibrium position.
The equation of motion of a particle is described by: OM t-1+(2)1 Determine the equation of trajectory of the particle and plot it on an xy coordinate system. a) b) At which point the motion starts. c) Determine the velocity vector and the acceleration vector of the particle in function of t d) Determine the tangential acceleration, the normal acceleration, and the radius of curvature in function of t. Is this a central acceleration, why or why not? At what...
Motion can be derived from the slope of the graph? 8 . Wild equation Show how position vs time and velocity vs time graphs are connected. Include the following information in your summary: • What are the 5 variables you need for accelerated motion problems? How do you determine the equation you will need to use to solve the problem? What are the accelerated motion kinematics equations? What do +/- mean for kinematics? What combinations of (+/-) velocity and acceleration...
Consider the system below, write the equation of motion and calculate the response assuming that the system does not have any initial displacement and is initially at rest. Additionally, for the values ki =500 N/m, k2 = 300 N/m, m= 100 kg, and F(t) = 10 sin(10) N. FC
The simple Harmonic motion equation for a 5 kg object attached to a spring is: X=.75 sin (4(pi)t + (pi/3)) a) What is its max velocity based on the equation? b) Check part a answer using Energy (show work)? c)What is the max force exerted on the object?
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE d²x 102 +w²x = Focos(yt) where Fo and wty are constants. Without worrying about those constants, answer the questions (a)-(b). (a) Show that the general solution of the given ODE is [2 pts] Fo x(t) == xc + Ip = ci cos(wt) + C2 sin(wt) +- W2 - 92 cos(7t). (b) Find the values of ci and c2 if the initial conditions are x(0) =...
A ball and spring system is moving with simple harmonic motion, described by the equation x=4cos(6πt), where x is in cm and t is in seconds. What is the maximum velocity of the ball?