A mass of 5 kg is suspended from a spring of stiffness 46 kN/m. A dashpot is fitted between the mass and the support with the amplitude reduction factor of 2. Determine a. The undamped frequency b. The damped frequency c. The critical damping coefficient

The maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil velocity is to be between 8 m/s and 10 m/s, find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least 500 kg.

An electric motor and its base have a combined mass of M = 12 kg. Each of the four springs attached to the base has a stiffness k =480 kN/m and a viscous damping coefficient c. The unbalance of the motor is equivalent to a mass m =0.005 kg located at the distance e=90mm from the center of the shaft.When the motor is running at ω = 400 rad/s, its steady-state amplitude is 1.8 mm.Determine (a) the damping coefficient of each spring; and (b) the phase anglebetween the displacement of the motor and ωt.

The spring-mass-damper system shown below has m1 = m2 = 3.4 kg and k = 97.7 N/m. In addition, a damping factor of 0.3 is given. The initial position and velocity of the system is x(t=0)=4.3 mm and x'(t=0)=0 m/s respectively. Frictionless pulley m2 Calculate the time required for the amplitude to reduce to 10% of the initial conditions.