Mechanical Vibr...

The displacement of particle undergoing S.H.M. follows the equation

where y is displacement in cm and t is the time. The maximum acceleration of the particle is approximately.

A mass of 100 kg is held between two springs as shown in figure. The natural frequency of vibration of the system in cycles/second is

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.

A spring mass system with mass 2 Kg and stiffness 3200 N/m has an initial displacement of x0 = 0. The maximum initial velocity that can be given to the mass without the amplitude of free vibration exceeding a value of 0.1m is

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 mass m is suspended from a spring of stiffness 4000 N/m and is subjected to a harmonic force having an amplitude of 100N and a frequency of 5Hz. The amplitude of the forced motion of mass is observed to be 20mm. The value of m is nearly

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).

The natural frequency (in rad/s) of vibration of the given system is

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)?

The circular disc of mass m and radius r is pivoted at point O as shown. If the disc is rotated by an angle ‘θ’ and is left to vibrate, the natural frequency [in rad/sec] of the vibration of the system is

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?

The natural frequency [in rad/s] of vibration of spring mass system shown in the figure is

In viscous damping, to which parameter is the damping force proportionally related?

In under-damped vibrating system, if X1 and X2 are successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to which of the following?