Mechanical Vibrations Questions and Answers – Free Vibration of Single Degree of Freedom Systems

This set of Mechanical Vibrations Multiple Choice Questions & Answers (MCQs) focuses on “Free Vibration of Single Degree of Freedom Systems”.

1. Free Vibrations occur in the absence of an external excitation
a) Yes
b) No
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2. When the block is drawn from its equilibrium position, a potential energy developed in the—-

a) Spring
b) Block
c) Spring is kx²
d) Block is kx2/²
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3.The differential equation governing free vibrations of a linear system are derived in the form——
a) m_eq x.. + c_eq x. + k_eq x = 0
b) c_eq x.. + m_eq x. + k_eq x = 0
c) m_eq x.. – c_eq x. + k_eq x = 0
d) m_eq x.. + k_eq x. + c_eq x = 0
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4. Free Vibrations of a Single Degree of Freedom system are described by a ——————-
a) Homogenous First order differential equation
b) Homogenous Second order ordinary differential equation
c) Cartesian equation
d) First order differential equation
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5. Free Vibrations are the result of a kinetic energy imparted to the system
a) True
b) False
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Common data questions from 6 to 8

The differential equation governing free vibrations of a linear system are derived in the form
m_eq x.. + c_eq x. + k_eq x = 0

6. The Second derivative term is due to—–
a) External forces
b) Velocity
c) Inertia Forces
d) Displacement
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7. The first derivative term is due to ——-
a) Velocity
b) Viscous damping
c) Elastic forces
d) Displacement
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8. The Zeroth derivative term is due to
a) Velocity
b) Viscous damping
c) Elastic forces
d) Displacement
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9. The differential equation governing free vibrations of a linear system are derived in the parameters damping ratio, natural frequency is———–
a) x.. – 2 ζ ωn x. – ωn² x = 0
b) x.. + 2 ζ ωn x. – ωn² x = 0
c) x.. – 2 ζ ωn x. + ωn² x = 0
d) x.. + 2 ζ ωn x. + ωn² x = 0
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Common data questions from 10 to 12
The differential equation governing free vibrations of a linear system are derived in the form
m_eqx.. + c_eq x. + k_eq x = 0

10. If the energy method is used to derive the differential equation, the Second derivative term is due to—–
a) External forces
b) Kinetic Energy
c) Inertia Forces
d) Displacement
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11. The first derivative term is due to ——-
a) Viscous friction forces
b) Viscous damping
c) Elastic forces
d) Displacement
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12. The Zeroth derivative term is due to
a) Potential Energy
b) Viscous damping
c) Elastic forces
d) Displacement
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Common data for question 13 & 14

The differential equation governing the single degree of freedom system is 5x.. + 4 x. + 7 x = 0

13. Find the natural frequency of motion
a) 3.183
b) 2.183
c) 1.183
d) 0.183
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The natural frequency of motion is given by ωn = √ ( keq/meq)
Substituting the values, we have  ωn  = √(7/5)
                                      = 1.183 rad/s

14. Find the damping ratio
a) 0.008
b) 0.338
c) 0.118
d) 0.228
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The damping ratio is given by ζ  = ceq / ( 2 √(k<sub>eq</sub>m<sub>eq</sub>) )
Substituting the values, we have , ζ  = 4 / ( 2 √ (7×5))
                                      = 0.338

15. The differential equation governing the angular oscillation of the compound pendulum is

a) m (L²/3) ӫ – mg (L/2) sin ө
b) m (L²/3) ӫ + mg (L2/2) sin ө
c) m (L/3) ӫ + mg (L/2) sin ө
d) m (L²/3) ӫ + mg (L/2) sin ө
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Sanfoundry Global Education & Learning Series – Mechanical Vibrations.

To practice all areas of Mechanical Vibrations, here is complete set of Multiple Choice Questions and Answers.