What is the action associated with the full period of a two-dimensional isotropic oscillator? Discuss your result. Please explain in detail.

A two degree of freedom undamped system has natural frequencies 2 rad/s and 3 rad/s and corresponding mode shapes {{{ and . A damping ratio of 2% is assumed for both modes. The initial displacement is {mm and initial velocity is {mm/s. The displacement of the first degree of freedom in mm at time t=3 s is 0.3141 O 0.5686 0.1533 0.1543

PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) m (2) {2} cm. = cm, v (0) Sec 00000 m k 00000 k x₂ (1) 5k 0000 Figure 3 00000 k x₂ (1) m 00000 k X3 (1)

Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping?  Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant.  Using c=5.0, what is the new period of oscillation.  What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.

Find the natural response of the following spring–mass system with m=1,k= 1 and the initial position and velocity being both equal to 1.     Please answer in typing format please

Vibrations