Oscillations Part 2

From the potential energy curve, $U_{\max}=\frac{1}{2}kA^{2}$ $10=\frac{1}{2}k(2)^{2}$ ⇒ k = 5 N / m The length of the simple pendulum, L = 4 m Time period of spring, $T=2\pi\sqrt{\frac{k}{m}}$ Time period of simple pendulum, $T=2\pi\sqrt{\frac{I}{g}}$ The time period of simple pendulum is same as the time period ofthe spring oscillation. $\Rightarrow 2\pi\sqrt{\frac{I}{g}}=2\pi\sqrt{\frac{k}{m}}$ Substituting the values in the above equations, we get $2\pi\sqrt{\frac{4}{g}}=2\pi\sqrt{\frac{5}{5}}$ $g=4\text{ m/s}^2$ ∴ The acceleration due to the gravity on the planet is $4\text{ m/s}^2$.