Mechanical Vibration Part-2

 $3\frac{\text{d}^2x}{\text{d}y^2}+9\frac{\text{d}x}{\text{d}y}+27x=0$  is the equation of motion for a damped viscous vibration. The damping factor is

• 0.25

• 0.5

• 0.75

• 1.0

In a forced vibration with viscous damping, maximum amplitude occurs when forced frequency is

• Equal to natural frequency

• Slightly less than natural frequency

• Slightly greater than natural frequency

• Zero

When the mass of a critically damped single degree of freedom system is deflected from its equilibrium position and released, it will

• return to equilibrium position without oscillation

• Oscillate with increasing time period

• Oscillate with decreasing amplitude

• Oscillate with constant amplitude.

Under logarithmic decrement, the amplitude of successive vibrations are

• Constant

• in arithmetic progression

• In geometric progression

• in logarithmic progression

If air resistance is neglected, while it is executing small oscillations the acceleration of the bob of a simple pendulum at the mid-point of its swing will be

• zero

• a minimum but not equal to zero

• a maximum

• not determinable unless the length of the pendulum and the mass of the bob are known

A machine mounted on a single coil spring has a period of free vibration of T. If the spring is cut into four equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration of the new system will become.

• 16T

• 4T

• $\frac{T}{4}$

• $\frac{T}{16}$

A uniform cantilever beam undergoes transverse vibrations. The number of natural frequencies associated with the beam is

• 1

• 10

• 100

• $\infty$

Consider the following methods:

1. Energy method 2. Equilibrium method 3. Rayleigh's method

Which of these methods can be used for determining the natural frequency of the free vibrations?

• 1 & 2

• 2 & 3

• 3 & 1

• 1, 2 & 3

The transmitted force through a mass-spring damper system will be greater than the transmitted through rigid supports for all values of damping factors, if the frequency ratio  $\frac{\omega}{\omega_n}$  is

• more than  $\sqrt{2}$  

• less than  $\sqrt{2}$  

• equal to one

• less than one

A spring-mass suspension has a natural frequency of 40 rad/s. What is the damping ratio required if it is desired to reduce this frequency to 20 rad/s by adding a damper to it?

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{4}$