The period of a simple harmonic oscillator is given by
[tex]T=2\pi\sqrt[]{\frac{m}{k}}[/tex]
Then, if k = 5 and the period has to be 6 seconds, we can find the mass m as:
[tex]\begin{gathered} T=2\pi\sqrt[]{\frac{m}{k}} \\ \frac{T}{2\pi}=\sqrt[]{\frac{m}{k}} \\ (\frac{T}{2\pi})^2=\frac{m}{k} \\ m=k\cdot(\frac{T}{2\pi})^2 \\ m=5\cdot(\frac{6}{2\pi})^2 \\ m\approx5\cdot(0.955)^2 \\ m\approx5\cdot0.912 \\ m\approx4.56 \end{gathered}[/tex]
NOTE: as T is in seconds, we assume standard units for the constant k. Then, the mass is in kg.
Answer: the mass has to be approximately 4.56 kg.
