Homework Problem $24$

Name:

Phys $213$ Fall $2024$

A mass mi $=0\mathrm{.}540$ kg is attached to the end of a light string of length L $=2\mathrm{.}50$ m$,$ forming a

simple pendulum that undergoes small oscillations. Separately, a mass m$2=0\mathrm{.}300$ kg 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.

b$)$ Find the period T$.$

c$)$ Suppose that the masses are now swapped, so that m$2$ is attached to the string and mi 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