$E_{p} = 8.67, mathrm{J}$

/$x = 247, mathrm{mm} = 0.247, mathrm{m}$

Energy is given by:

$$
E_{p} = dfrac{1}{2}kx^{2}
$$

We can express spring constant as:

$$
k= dfrac{E}{1/2x^{2}}
$$

When we put known values into the previous equation we get:

$$
k = dfrac{8.67, mathrm{J}}{1/2 cdot (0.247, mathrm{m})^{2}}
$$

$$
boxed{k = 284, mathrm{N/m}}
$$

$k = 275, mathrm{N/m}$

$x = 14.3, mathrm{cm} = 0.143, mathrm{m}$

Force is given by:

$$
F = kx
$$

When we put known values into the previous equation we get:

$$
F = 275, mathrm{N/m} cdot 0.143, mathrm{m}
$$

$$
boxed{F = 39.3, mathrm{N}}
$$

$m = 30.4, mathrm{g} = 0.0304, mathrm{kg}$

$x = 0.85, mathrm{m}$

We can determine spring constant by using Newton’s second law:

$$
kx = mg
$$

$g$ is gravitational acceleration which value is known $g = 9.81, mathrm{“m/s^{2}}$

$k$ will be:

$$
k = dfrac{mg}{x}
$$

When we put known values into the previous equation we get:

$$
k = dfrac{0.0304, mathrm{m} cdot 9.81, mathrm{m/s^{2}}}{0.85}
$$

$$
boxed{k = 0.35, mathrm{N/m} }
$$

$E = (1/2)*(350)*(0.85 – 0.050)^2$

$$
E = 112 N.m
$$

$T^2 = (2 pi)^2 (dfrac{l}{g})$

$dfrac{l}{g} = dfrac{T^2}{(2 pi)^2}$

$$
l = dfrac{T^2 g}{(2 pi)^2}
$$

$T = 3, mathrm{s}$

Frequency is given by:

$$
f = dfrac{1}{T}
$$

When we put known values into the previous equation we get:

$$
f = dfrac{1}{3, mathrm{s}}
$$

$$
boxed{f = 0.3, mathrm{1/s} = 0.3, mathrm{Hz}}
$$

$v = dfrac{2 d}{t} = dfrac{(2)*(11.2)}{4} = 5.6 m/s$

The frequency of the wave:

$$
f = dfrac{v}{lambda} = dfrac{5.6}{1.2} = 5 Hz
$$

$l = dfrac{T^2 g}{(2 pi)^2}$

$l = dfrac{(4.89)^2 (9.80)}{((2) (3.1416))^2}$

$$
l = 5.94 m
$$

$k x = m g$

Solve for k:

$k = dfrac{m g}{x}$

Where:

the units of m = [m] = kg

the units of g = [g] = $dfrac{m}{s^2}$

the units of x = [x] = meters = m

Thus:

$[k] = dfrac{[m] [g]}{[x]}$

$[k] = dfrac{(kg) (m/s^2)}{m}$

$[k] = dfrac{kg}{s^2}$