Mechanical Vibr...

A vibrating system consists of a mass of 50 kg, a spring with a stiffness of 30 kN/m and a damper. The damping provided is only 20% of the critical value. Determine the natural frequency of damped vibration.

The equation of motion of a forced damped vibration system is given as \(3\ddot x + 9\dot x + 27x = 0\), The damping factor is_______

For steady-state forced vibrations what is the phase difference at resonance (in degrees) _____?

A spring mass system has natural frequency of 5 rad/s and damping factor is 0.3. What is ratio of 2 successive amplitudes of vibration?

A mass of 0.5 kg is suspended in a vertical plane by a spring having a stiffness coefficient of 300 N/m. If the mass is displaced downward from its static equilibrium position through a distance 0.01 m, determine the natural frequency of the system.

The equation of motion for a single degree of freedom system with viscous damping is \(16\ddot x + 5\dot x + 4x = 0\). The damping ratio of the system is

In a system with a rotating unbalance of 1 kg at a radius of 1 cm rotates at very large speed, much above resonance speed. The mass of system is 100 kg. The amplitude of vibration will be in order of ____

A cantilever beam of cross section area ‘A’, moment of Inertia I and length ‘L’ is having natural frequency ω₁. If the beam is accidentally broken into two halves, the natural frequency of the remaining cantilever beam ω₂ will be such that 

In an experiment a student by mistake took a force with excitation frequency. √2 times the natural frequency what do we expect his calculated transmissibility be?

A damped mass spring system has mass of 10 kg, spring stiffness of 4000 N/m and damping coefficient of 40 Ns/m. The amplitude of forcing function, F₀ is 60 N and the forcing frequency is 40 rad/sec. Determine the amplitude of the force transmitted to the support (in N).

Two heavy rotors are mounted on a shaft. Considering each rotor separately the transverse natural frequencies obtained are 200 Hz and 310 Hz respectively. What is the lowest critical speed (rpm)?

A steel shaft of diameter 2 cm carries a disc of mass 19.2 kg supported in long bearings at it’s mid span of length 0.5 m. The critical speed of shaft (rpm) is ____ (Both the ends are fixed)

(E = 200 GPa)

A machine weighing 4 kg is vibrating in a fluid medium. Harmonic force of magnitude 50 N acts on it and produces resonance amplitude of 20 mm with frequency of 12 Hz. The value of damping coefficient is ________Ns/m

A 45 kg machine is mounted on four parallel springs each of stiffness 0.2 MN/m. When machine operates at 32 Hz, the machine’s steady state amplitude is measured as 1.5 mm. What is magnitude of excitation force provided to the machine at this speed?

In a spring mass system, the mass is 0.2 kg and the stiffness of the spring is 1 kN/m. By introducing a damper of damping coefficient 8.5 Ns/m, by what percentage will the frequency of oscillation change w.r.t. original value?