Oscillations and Waves
Beginner
Simple harmonic oscillation
Source: High school physics (Chinese)
Problem
A 2.0 kg object hangs from a spring. When an additional 0.3 kg object is hung below it, the spring stretches a further 2.0 cm. The 0.3 kg object is then removed and the 2.0 kg object is set into vibration.
Find the period of the oscillation. (Take $g = 9.8$ m/s$^2$.)
$k = 147$ N/m; $T \approx 0.73$ s.
The added 0.3 kg weight produces the extra stretch $\Delta x = 0.020$ m, so the spring constant is $k = \dfrac{0.3 \times 9.8}{0.020} = 147$ N/m. The 2.0 kg mass then oscillates with period $T = 2\pi\sqrt{\dfrac{m}{k}} = 2\pi\sqrt{\dfrac{2.0}{147}} \approx 0.73$ s.