Part $($b$)$ Write an equation for the work necessary to stretch the spring from the relaxed state to a distance x$1.$

Expression$$:

W$1=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Select from the variables below to write your expression. Note that all variables may not be required.

$,$ $,$ $,$ a$,$ d$,$ g$,$ h$,$ j$,$ k$,$ m$,$ P$,$ S$,$ t$,$ x$1,$ x$2$

Part $($c$)$ Calculate the work, in joules, required to stretch the spring from its relaxed state to the position x$1=54\mathrm{.}7$cm$.$

Numeric$$: A numeric value is expected and not an expression.

W$1=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$J

Part $($d$)$ Write an equation for the work necessary to stretch the spring from the position x$1$ to position x$2.$

Expression$$:

W$12=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Select from the variables below to write your expression. Note that all variables may not be required.

$,$ $,$ $,$ a$,$ d$,$ g$,$ h$,$ j$,$ k$,$ m$,$ P$,$ S$,$ t$,$ x$1,$ x$2$

Part $($e$)$ Calculate the work, in joules, required to stretch the spring from x$1=54\mathrm{.}7$cm to x$2=90\mathrm{.}8$cm$.$

Numeric$$: A numeric value is expected and not an expression.

W$12=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$J