A damped harmonic oscillator with m = 10 kg, k = 250 N/m, and c = 6 driving force given by F, cos ot, where F= 48 N. (a) What value of o results in steady-state oscillations with maximum ar condition: %3! %3D

: An undamped oscillator has a natural frequency of a rad/s. Damping is added to the system to give a damping factor equal to 0.30 s¬1. Find the corresponding Q – value and frequency of damped oscillations. 3 For a Damped Simple Harmonic Oscillator, wo? – w² = 10-w,?, where (w) is the frequency of DHO. Find Q, and the logarithmic decrement (A) of the system. If wo = 106 rad/s, Q, = 5 × 10² and m = 10-10kg, calculate the stiffness, and resistive constant (b) of the system. S For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force F4 = bv : ngular frequency (w) is given by: E = nbwA². 1

42. k= 1080N/m wwwwww 30 kg X = Ae 5.₂ ( F = 25cos wt (N) (a) A 30kg cart is acted upon by the harmonic force shown in the figure. If c = 0, determine the range of the driving frequency w for which the magnitude of the steady state response is less than 75mm Ans: [w 6.86rad/s] (b) If the driving frequency for the system is a = rad/s, determine the required value of the damping coefficient, C, if the steady state amplitude is not to exceed 75mm. Ans: [55.6 Ns/m²]