A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is d²x + wóx = a cos wt, dt2 where x is its position. Given that at t function x(t). Describe the solution if w is approximately, but not exactly, equal 0 we have x = dx/dt = 0, find the to wg.

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.

Example-3. Determine natural frequency, damped natural frequency, damping ratio and logarithmic decrement for the system as shown: 21 Neglect mass of rod m TWwwx THEATEFNT mummi