Questions without answers in Vibrations

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350 \mathrm{~N} \mathrm{~s} / \mathrm{m}$ and the damping c...

A $5$ kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of th...

A block of mass $1 \: kg$ connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping fa...

​​​​​The system shown in the figure below consists of a cantilever beam (with flexural rigidity $E I$ and negligible mass), a spring (with spring constant $K$ and negligi...

​​​​A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and the ampl...

A vibratory system consists of mass $m$, a vertical spring of stiffness $2 k$ and a horizontal spring of stiffness $k$. The end $\mathrm{A}$ of the horizontal spring is g...

The figure shows a block of mass $m=20 \mathrm{~kg}$ attached to a pair of identical linear springs, each having a spring constant $k=1000 \mathrm{~N} / \mathrm{m}$. The ...

For a dynamical system governed by the equation.$$\ddot{x}\left ( t \right ) + 2\zeta \omega _{n}\dot{x}\left ( t \right )+\omega _{n}^{2}x\left ( t \right ) = 0$$the dam...

A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequ...

Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= ...

A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolat...

Consider the system shown in the figure. A rope goes over a pulley. A mass, $\text{m}$, is hanging from the rope. A spring of stiffness, $\text{k}$, is attached at one en...

Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure.If the amplitude of the free vibration...

The equation of motion of a spring-mass-damper system is given by $$\dfrac{d^2x}{dt^2}+3 \dfrac{dx}{dt} +9x = 10 \sin(5t)$$The damping factor for the system is$0.25$$0.5$...

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains u...

A machine of mass $m=200 \: kg$ is supported on two mounts, each of stiffness $k=10 \: kN/m$. The machine is subjected to an external force (in $N$) $F(t) = 50 \cos 5t$. ...

Which of the following statements are TRUE for damped vibrations?P. For a system having critical damping, the value of damping ratio is unity and system does not undergo ...

A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the s...

In a spring-mass system, the mass is m and the spring constant is $k$. The critical damping coefficient of the system is $0.1$ $kg/s$. In another spring-mass system, the ...

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to...