**1. What does the degree of freedom represent in a mechanical system?**

a) The number of masses present

b) The number of independent coordinates needed to describe its configuration

c) The stiffness of the system

d) The damping coefficient of the system

**Explanation:** The degree of freedom in a mechanical system refers to the number of independent coordinates required to define its configuration. It determines the system’s complexity and the number of variables needed to describe its motion.

**2. In an undamped system, which of the following is true?**

a) There is no external force acting on the system

b) There is no friction or resistance to motion

c) The system has a natural frequency of oscillation

d) The system experiences a constant damping force

**Explanation:** In an undamped system, there is no friction or resistance to motion. This allows the system to oscillate indefinitely at its natural frequency without losing energy.

**3. What is the relationship between force and displacement in a mass-spring system?**

a) Linear

b) Quadratic

c) Exponential

d) Inverse square

**Explanation:** The relationship between force and displacement in a mass-spring system is linear, according to Hooke’s Law, which states that the force exerted by a spring is directly proportional to its displacement.

**4. What is the purpose of damping force in a mechanical system?**

a) To increase the amplitude of motion

b) To decrease the amplitude of motion

c) To increase the natural frequency

d) To decrease the stiffness of the system

**Explanation:** The damping force in a mechanical system is introduced to decrease the amplitude of motion by dissipating energy, thereby preventing the system from oscillating indefinitely.

**5. Which principle states that the sum of the external forces and the inertial forces acting on a system is zero?**

a) Newton’s Second Law

b) Hooke’s Law

c) D’Alembert’s Principle

d) Archimedes’ Principle

**Explanation:** D’Alembert’s Principle states that the sum of the external forces and the inertial forces (due to acceleration) acting on a system in equilibrium is zero. It is commonly used in dynamics to simplify the analysis of motion.

**6. How is the differential equation of motion solved for a mass-spring-damper system?**

a) Analytically

b) Numerically

c) Graphically

d) Geometrically

**Explanation:** The differential equation of motion for a mass-spring-damper system is typically solved analytically using techniques such as Laplace transforms or by numerical methods such as finite element analysis.

**7. What does the frequency of motion represent in a vibrating system?**

a) The rate of change of displacement with respect to time

b) The maximum displacement from equilibrium

c) The number of oscillations per unit time

d) The resistance to motion offered by the system

**Explanation:** The frequency of motion in a vibrating system represents the number of oscillations or cycles per unit time. It is measured in Hertz (Hz) and determines the pitch of the vibration.

**8. What is the period of motion in a vibrating system?**

a) The maximum displacement from equilibrium

b) The time taken to complete one full cycle of motion

c) The rate of change of displacement with respect to time

d) The damping coefficient of the system

**Explanation:** The period of motion in a vibrating system is the time taken to complete one full cycle of oscillation. It is the inverse of frequency and is measured in seconds.

**9. How does damping affect the amplitude of motion in a vibrating system?**

a) Damping increases the amplitude

b) Damping decreases the amplitude

c) Damping has no effect on the amplitude

d) Damping reverses the direction of motion

**Explanation:** Damping decreases the amplitude of motion in a vibrating system by dissipating energy, thereby reducing the magnitude of oscillations over time.

**10. What is the amplitude of motion in a vibrating system?**

a) The maximum displacement from equilibrium

b) The rate of change of displacement with respect to time

c) The frequency of motion

d) The period of motion

**Explanation:** The amplitude of motion in a vibrating system is the maximum displacement from the equilibrium position. It represents the peak value of the oscillation and is a measure of the system’s energy.