A block of mass $m=2.0\ \mathrm{kg}$ is attached to a spring whose force constant, $k$, is $300\ \mathrm{\displaystyle \frac{N}{m}}$.
Calculate the frequency and period of the oscillations of this spring‑block system.
$f=1.9\ \mathrm{Hz}$
$T=0.51\ \mathrm{s}$
One of the defining properties of the spring‑block oscillator is that the frequency and period can be determined from the mass of the block and the force constant of the spring. The equations are as follows:
$$f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$$
$$T=2\pi \sqrt{\frac{m}{k}}$$
Therefore,
$$f=\frac{1}{2\pi }\sqrt{\frac{300\ \mathrm{\displaystyle \frac{N}{m}}}{2.0\ \mathrm{kg}}}$$
$$f=1.9\ \mathrm{Hz}$$
$$T=2\pi \sqrt{\frac{2.0\ \mathrm{kg}}{300\ \mathrm{\displaystyle \frac{N}{m}}}}$$
$$T=0.51\ \mathrm{s}$$
Notice that $f\approx 2\ \mathrm{Hz}$ and $T\approx 0.5\ \mathrm{s}$, and that these values satisfy the basic equation $T=\displaystyle \frac{1}{f}$.