18.1.3. Analogy with Free Vibration

Try these first

1. 1.

   What is the purpose of the inertial force in a mass-spring system?

   Hint

   Think about Newton's second law.

2. 2.

   What kind of equation describes the motion of a free vibrating system?

   Hint

   Can you remember the standard form for these equations?

3. 3.

   What is the relationship between mass and inertial force?

   • Mass is not related to inertial force
   • Inertial force is proportional to mass
   • Inertial force decreases with mass

   Hint

   Recall F=ma from Newton's second law.

4. 4.

   True or False: The characteristic equation can help determine a system's natural frequency.

   • True
   • False

   Hint

   Think about why frequencies are important in vibrational analysis.

5. 5.

   Consider a mass-spring system with m1 = 2 kg, m2 = 3 kg, and spring constants k1 = 100 N/m and k2 = 200 N/m. Derive the equations of motion and identify the natural frequencies.

   Hint

   Utilize the characteristic equation for finding frequencies.

6. 6.

   Explore how the system reacts when applied forces are changed. How would you expect the behavior to differ with increased stiffness?

   Hint

   Visualize the difference in a stiffer vs. looser spring.