Given:
The mass of the pendulum, m=1.29 kg
The length of the simple pendulum, L=0.830 m
The period of the pendulum, T=1.809 s
To find:
(b) The spring constant of the spring so that the period of the oscillation of the spring will be T.
Explanation:
The period of oscillation of a spring-mass system is given by the equation,
[tex]T=2\pi\sqrt{\frac{m}{k}}[/tex]On rearranging the above equation,
[tex]\begin{gathered} T^2=4\pi^2(\frac{m}{k}) \\ \Rightarrow k=\frac{4\pi^2m}{T^2} \end{gathered}[/tex]On substituting the known values,
[tex]\begin{gathered} k=\frac{4\pi^2\times1.29}{1.809^2} \\ =15.56\text{ N/m} \end{gathered}[/tex]Final answer:
The spring constant of spring is 15.56 N/m