vibrations

A block of mass 1 kg connected to a spring of stiffness 10 N m⁻¹ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the dampe...

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

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 factor) is equal...

A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measur...

A vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k. The end A of the horizontal spring is given a horizontal motion x_A...

The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizo...

A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The...

A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force trans...

Consider the system shown in the figure. A rope goes over a pulley. A mass, m, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope i...

The natural frequencies corresponding to the spring-mass systems I and II are ω_I and ω_II, respectively. The ratio $\frac{\omega_I}{\omega_{II}}$ is

A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For t...

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

The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x}+Kx= F \cos(\omega t)$, where M is the mass, K is the spring stiffness, F is the force ampl...

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 underdamped...

The damping ratio for a viscously damped spring mass system, governed by the relationship $m\frac{d^2x}{dt^2} + c\frac{dx}{dt} + kx = F(t)$, is given by

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. Assuming only vertica...

A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L/3 from one of its ends. The bar is further supported using springs, each of stiffne...

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 mass is $...

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g moon = g earth /6) is

In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original valu...

The suspension system of a two-wheeler can be equated to a single spring-mass system with a viscous damper connected in series. Sketch the free body diagram and give the equations...