A $30\mathrm{.}0-$cm$-$long spring is hanging vertically. When a $100\mathrm{.}0-$g object is attached to the bottom end of the spring, the spring is stretched to a new length of $34\mathrm{.}5$ cm$.$

$1.)$ What is the spring constant in N$/$m$?$

$2.)$ How much is the spring displaced $($in cm$)$ if a $50\mathrm{.}0-$g object is attached to the spring?

$3.)$ Attach a $200\mathrm{.}0-$g object to the spring and allow the spring$-$object system to reach its equilibrium state. Pull down the object by $3\mathrm{.}0$ cm then release. What is the period of the oscillation in s$?$

$4.)$ What is the period of the oscillation if the $200\mathrm{.}0-$g object is pulled down $5\mathrm{.}0$ cm from the spring$-$object equilibrium level?

$5.)$ To experimentally determine the period of an oscillation described in step c or d above, why is it better to measure the time for multiple oscillations $($e$.$g$.,10$ oscillations$)$ instead of just one oscillation? How does a person$$s reaction time affect the uncertainty in the measurements?