Problem 4Q

Real springs have mass. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

Solution 4Q

How does period of a spring with mass change when we assume that spring has mass as against when it is an ideal spring?

The real spring has mass, so the effective mass oscillating at the end of a real spring is higher than for an ideal spring.

Frequency is inversely proportional to square root of mass as given by the formula below.

Thus, the frequency will be smaller for a real spring compared to that of an ideal spring.

Since f = 1/T, the true period will be larger than the ideal period.