This set of Mechanical Vibrations Multiple Choice Questions & Answers (MCQs) focuses on “Free Vibrations of an Undamped Translational System”.

1. The equation of motion for following system is

a) m x.. – kx = 0

b) m x.. + kx^{2} = 0

c) k x.. + mx = 0

d) m x.. + kx = 0

View Answer

Explanation: Newton’s second law states that product of mass and acceleration is the resultant force on the mass. The application of this to the above system yields the equation of motion m x.. + kx = 0 where x.. = d

^{2}x/dt

^{2}

2. For the following spring- mass system, what is the circular natural frequency ?

a) (k/m)(1/^{2})

b) m^{2}/k

c) m/k

d) k/m

View Answer

Explanation: According to the figure, spring mass system is in vertical position, the circular natural frequency for this type of system is ω

_{n}= (k/m)(1/

^{2})

3. The undamped natural frequency depends on initial conditions of motion.

a) True

b) False

View Answer

Explanation: The undamped natural frequency depends on mass and stiffness , does not depends on initial conditions or amplitude of motion.

4. The spring constant k can be expressed in terms of m for spring-mass system in vertical position is———-

a) mg/δ_{st}

b) 2mg/δ_{st}

c) δ_{st}/mg

d) δ_{st}/2mg

View Answer

Explanation: The spring constant k can be expressed in terms of the massm from ω

_{n}(1/2) k = w/δ

_{st}stst(1/2).Thus it is not necessary that we know the spring stiffness and mass.

6. The equation of motion for spring- mass system can also be derived by the conservation of energy principle.

a) Yes

b) No

View Answer

Explanation: It can also derived by the conservation of energy, in this kinetic energy T is stored in the mass and potential energy U in stored in the spring.

7. The natural period of vibration of spring-mass system in vertical position is———-

a) 2п( δst/2g)^{(1/2)}

b) 2п( 2δst/g)^{(1/2)}

c) 2п( δst/g)^{(1/2)}

d) п( δst/g)^{(1/2)}

View Answer

Explanation: The natural period is given by Tn = 1/fn

The natural frequency in cycles per second is given by fn = 1/2п (g/δst )

^{(1/2)}

Tn = 1/fn = 2п( δ

_{st}(1/2)

8. Given spring constant of the hoisting system is k_{eq}2d2)/( Πb^{2}d^{2} + lat^{3}) ).

Find the natural frequency of vibration in vertical direction of hoisting system

a) [ ( Eg/4w) × ×( (Πat^{2}d^{2}d^{3} + lat^{3}) ).

b) [ ( Eg/4w) – ( (Πat^{2}d^{2}d^{3} + lat^{3}) ).^{1/2
c) [ ( Eg/4w) + ( (Πat2d)/(Πb2d3 + lat3) ).1/2
d) [ ( Eg/4w) × ( (Πat2d)/(Πb2d3 + lat3) ).1/2
View Answer}

Explanation: The natural frequency of vibration in the vertical direction of hoisting system is

ω

_{n}= (k

_{eq}/m)

^{1/2}= ωn = (k

_{eq}g/w)(1/2) = [ ( Eg/4w) × ( (Πat

^{2}d

^{2}d

^{3}+ lat

^{3}) ).

^{1/2}

9. According to the conservation of energy principle , relation between kinetic energy and potential energy is—-

a) summation of kinetic energy and potential energy is constant

b) both are equal

c) difference between kinetic energy and potential energy is zero

d) summation of kinetic energy and potential energy is zero

View Answer

Explanation: We can derive the equation of motion using conservation of energy principal. The kinetic energy T is stored in the mass and potential energy U is stored in the spring. T + U = constant.

10. The equation of motion for simple spring-mass system is m x.. + kx = 0 . If the gravity effects are induced , the equation is———–

a) x(t) = x(0) sin ωn t + (x. (0)/ ω_{n} ) sin ω_{n} t

b) x(t) = x(0) cos ωn t + (x. (0)/ ω_{n} ) sin ω_{n} t

c) x(t) = x(0) cos ωn t + (x. (0)/ ω_{n} ) cos ω_{n} t

d) x(t) = x(0) cos ωn t – (x. (0)/ ω_{n} ) sin ω_{n} t

View Answer

Explanation: x(t) = x(0) cos ω

_{n}t + (x. (0)/ ω

_{n}) sin ωn t, where x(0) is the initial displacement from the equilibrium position and x. (0) is the initial velocity.

**Sanfoundry Global Education & Learning Series – Mechanical Vibrations.**

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