Chapter 11, Problem 2Q

To determine

If the true period and frequencylarger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring since real spring have mass.

Answer to Problem 2Q

Solution:

The period will be larger, and the frequency will be smaller.

Explanation of Solution

Since the spring has mass, it must move its own mass as well as the mass at the end of the string. The greater the mass, the lower the frequency and the longer the period.

Since the real spring has mass, the mass that is moving is greater than the mass at the end of the spring. This larger mass will result in a smaller frequency. Thus, the true frequency will be smaller than the massless spring approximation. And since the true frequency is smaller, the true period will be larger than the massless spring approximation.

Conclusion:

The greater the mass, the lower the frequency and the longer the period.