Harmonic oscillator

Calculate the total energy of a body performing a harmonic oscillating motion if its mass is 200 g, the amplitude of the deflection is 2 cm and the frequency is 5 Hz. Round the result to 3 decimal places.

Correct answer:

E =  0.0395 J

Step-by-step explanation:

$$\begin{gathered} m=200\text{g}\to \text{kg}=200:1000\text{kg}=0.2\text{kg} \\ x=2\text{cm}\to \text{m}=2:100\text{m}=0.02\text{m} \\ f=5\text{Hz} \\ g=9.81{\text{m/s}}^2 \\ T=1/f=1/5=\frac{1}{5}=0.2\text{s} \\ \omega =2\pi \cdot f=2\cdot 3.1416\cdot 5\doteq 31.41591\text{/rad} \\ f=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{m}} \\ k={\omega }^2\cdot m=31.4159^2\cdot 0.2\doteq 197.3921 \\ E=\frac{1}{2}\cdot k\cdot x^2=\frac{1}{2}\cdot 197.3921\cdot 0.02^2=0.0395\text{J} \end{gathered}$$

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