7.9. Effect of Mass and Stiffness

Try these first

1. 1.

   What happens to the natural frequency if mass is increased?

   Hint

   Remember the inverse relationship.

2. 2.

   How does increasing stiffness affect vibration speed?

   Hint

   Recall the acronym discussed in class.

3. 3.

   What effect does increasing mass have on natural frequency?

   • Increases it
   • Decreases it
   • No effect

   Hint

   Recall the relationship we discussed.

4. 4.

   True or False: Increasing stiffness leads to a decrease in natural frequency.

   • True
   • False

   Hint

   Think about the impact of stiffness.

5. 5.

   A suspension bridge has a mass of 2000 kg and a stiffness of 12000 N/m. Calculate its natural frequency.

   Hint

   Use the formula for natural frequency.

6. 6.

   A designer needs to increase the stiffness of a structure to ensure it vibrates at a different frequency. If the current stiffness is 5000 N/m and mass remains constant at 1000 kg, what stiffness would achieve a natural frequency of 3 rad/s?

   Hint

   Rearrange the formula accordingly.