A mass m $=1\mathrm{.}15$ kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A $=8\mathrm{.}5$ cm and a

frequency f $=1\mathrm{.}75$ Hz$.$

Part $($a$)$

Write an equation for the spring constant k in terms of the variables in the problem statement $($that is to say, only use the variables and do not concern yourself with the assigned values$).$

k$=$

$0$

f

b

$1.$

n

P

JT

d h

m t

$8)$

M$^$J$456$

$12$

$(3$

HOME$)$

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Part $($b$)$

Calculate the spring constant k$,$ in newtons per meter.

Part $($c$)$

Write an equation for the total mechanical energy, E$,$ of the motion in terms of the variables in the problem statement $($that is to say, only use the variables and do not concern yourself with the assigned values$).$

Part $($d$)$

Calculate the total mechanical energy E$,$ in joules.