Question

Vibrations
A horizontal frictionless mass-spring system is set to oscillate at 10 Hz. If the spring constant is 450 N/m, what is the mass of the object?

Answer 1

Answer on Question #50089 – Physics - Mechanics | Kinematics | Dynamics

Vibrations

A horizontal frictionless mass-spring system is set to oscillate at $10\,\mathrm{Hz}$. If the spring constant is $450\,\mathrm{N/m}$, what is the mass of the object?

Solution:

$$\begin{array}{l} f = 10\,\mathrm{Hz} - \text{frequency}; \\ k = 450\,\frac{\mathrm{N}}{\mathrm{m}} - \text{spring constant}; \\ \mathrm{m} - \text{mass of the object}; \end{array}$$

Formula for the frequency for the mass-spring system:

$$f = \frac{1}{T} = \frac{1}{2\pi \sqrt{\frac{\mathrm{m}}{k}}}$$ $$2\pi f \sqrt{\frac{\mathrm{m}}{k}} = 1$$ $$4\pi^2 f^2 \mathrm{m} = k$$ $$\mathrm{m} = \frac{k}{4\pi^2 f^2} = \frac{450\,\frac{\mathrm{N}}{\mathrm{m}}}{4 \cdot 3.14 \cdot (10\,\mathrm{Hz})^2} = 0.36\,\mathrm{kg}$$

Answer: mass of the object is equal to $0.36\,\mathrm{kg}$.

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