TPR AP Oscillations Example 5 11558

A block oscillating on the end of a spring moves from its position of maximum spring stretch to maximum spring compression in $0.25\ \mathrm{s}$.

Determine the period and frequency of this motion.

$f=2\ \mathrm{Hz}$

The period is defined as the time required for one full cycle. Moving from one end of the oscillation region to the other is only half a cycle. Therefore, if the block moves from its position of maximum spring stretch to maximum spring compression in $0.25\ \mathrm{s}$, the time required for a full cycle is twice as much; $T=0.5\ \mathrm{s}$. Because frequency is the reciprocal of period, the frequency of the oscillations is

$$f=\frac{1}{T}$$

$$f=\frac{1}{(0.5\ \mathrm{s})}$$

$$f=2\ \mathrm{Hz}$$