A mass $m_1=0\mathrm{.}540kg$ is attached to the end of a light string of length $L=2\mathrm{.}50m,$ forming a simple pendulum that undergoes small oscillations. Separately, a mass $m_2=0\mathrm{.}300kg$ is attached to a horizontal spring on a frictionless surface. Both systems are set into simple harmonic motion with the same period $T.$ Assume that we can ignore friction.

a$)$ Find the spring constant of the spring.

$k=$

b$)$ Find the period $T.$

$7$

c$)$ Suppose that the masses are now swapped, so that $m_2$ is attached to the string and $m_1$ is attached to the spring, and each system is again set into simple harmonic motion. After swapping the masses, would the periods still be the same? Justify your answer.

Yes $$ No