# Recent questions tagged springs

A rigid mass-less rod of length $L$ is connected to a disc (pulley) of mass $m$ and radius $r = L/4$ through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness $2k$ is attached to the rod at its mid-span. An ... $\sqrt{3}\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{k}{m}}$
A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in the figure. For the system to be critically damped, the ratio $c/\sqrt{km}$ should be $2$ $4$ $2 \sqrt{7}$ $4 \sqrt{7}$
The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $2 \\$ $4$
If the wire diameter of a compressive helical spring is increased by $2 \%$, the change in spring stiffness (in $\%$) is _____ (correct to two decimal places)
The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x} + K x = F \cos(\omega t)$, where $M$ is the mass, $K$ is the spring stiffness, $F$ is the force amplitude and $\omega$ is the angular frequency of excitation. Resonance occurs when $\omega$ ... $\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{M}} \\$ $2 \pi \sqrt{\dfrac{K}{M}} \\$ $\sqrt{\dfrac{K}{M}}$
A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is $24$MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is __________.
A mass $m$ is attached to two identical springs having spring constant $k$ as shown in the figure. The natural frequency $\omega$ of this single degree of freedom system is $\sqrt{\dfrac{2k}{m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{4k}{m}}$
A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\dfrac{L}{3}$ from one of its ends. The bar is further supported using springs, each of stiffness $k$, located at the two ends. A particle of mass $m=\dfrac{M}{4}$ is fixed at one end of ... is $\sqrt{\dfrac{5k}{M}} \\$ $\sqrt{\dfrac{5k}{2M}} \\$ $\sqrt{\dfrac{3k}{2M}} \\$ $\sqrt{\dfrac{3k}{M}}$
The damping ratio for a viscously damped spring-mass system, governed by the relationship $m \dfrac{d^{2}x}{dt^{2}}+c\dfrac{dx}{dt}+kx=F(t)$, is given by $\sqrt{\dfrac{c}{mk}} \\$ $\dfrac{c}{2\sqrt{km}} \\$ $\dfrac{c}{\sqrt{km}} \\$ $\sqrt{\dfrac{c}{2mk}}$
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________
The static deflection of a spring under gravity, when a mass of $1 \:kg$ is suspended from it, is $1 \: mm$. Assume the acceleration due to gravity $g =10 \: m/s^2$. The natural frequency of this spring-mass system (in $rad/s$) is_____________
The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.
A single degree of freedom mass-spring-viscous damper system with mass $m$, spring constant $k$ and viscous damping coefficient $q$ is critically damped. The correct relation among $m$, $k$, and $q$ is $q=\sqrt{2km} \\$ $q=2\sqrt{km} \\$ $q=\sqrt{\dfrac{2k}{m}} \\$ $q=2\sqrt{\dfrac{k}{m}}$
A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $M$ and the spring constant is $K$. The polar moment ... $\displaystyle{\sqrt{\frac{2K(a+d)^2}{Ma^2}}} \\$ $\displaystyle{\sqrt{\frac{K(a+d)^2}{Ma^2}}}$
A single degree of freedom spring mass system with viscous damping has a spring constant of $10$ $kN/m$. The system is excited by a sinusoidal force of amplitude $100$ $N$. If the damping factor (ratio) is $0.25$, the amplitude of steady state oscillation at resonance is ________$mm$.
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is _______