The total mechanical energy $E$ of an oscillator can be expressed as the maximum potential energy or the maximum kinetic energy. Maximum potential energy: $E = \frac{1}{2} k A^2$ Maximum kinetic energy: $E = \frac{1}{2} m v_{max}^2$

[Q1] The spring constant $k$ can be found from the total energy and amplitude:

$$k = \frac{2E}{A^2} = \frac{2(1.0)}{(0.10)^2} = 200 \, \text{N/m}$$

[Q2] The mass $m$ can be found from the total energy and maximum velocity:

$$m = \frac{2E}{v_{max}^2} = \frac{2(1.0)}{(1.0)^2} = 2.0 \, \text{kg}$$

[Q3] The frequency $f$ can be found from the angular frequency $\omega$. We know $v_{max} = A\omega$, so $\omega = v_{max}/A$. The frequency is $f = \omega/(2\pi)$.

$$f = \frac{v_{max}}{2\pi A} = \frac{1.0}{2\pi (0.10)} = \frac{5}{\pi} \, \text{Hz}$$