Consider the mass-spring and damping system as shown in the figure. A harmonic force F = F0sin ωt acts upon the 11-kg mass. The spring constant is 7093 N/m and the damping coefficient is 252 N.s/m. There is no friction between the small rollers and the horizontal surface. Let F0  =923 N and ω = 117 rad/s. Calculate the period (in seconds) of the steady state vibrations. a) There is no frequency of free vibration, because there is damping. b) 0.2772 c) 0.1301 d) 0.2474 e) 0.0537

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.