Answer
See answer.
Work Step by Step
a.Find the period and frequency using the mass and the spring constant.
$$T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{\frac{0.885\;kg}{184\;N/m}}\approx 0.436\;s$$
$$f=1/T=2.29\;Hz$$
b. The initial speed is the maximum speed. Find the amplitude.
$$v_{max}=A\sqrt{\frac{k}{m}}$$
$$A = v_{max}\sqrt{\frac{m}{k}}= (2.26\;m/s) \sqrt{\frac{0.885\;kg}{184\;N/m}}\approx 0.157\;m$$
c. Find the maximum acceleration from the mass, the spring constant, and the amplitude.
$$a_{max}=Ak/m=(0.1567\;m)(184\;N/m)/(0.885\;kg)=32.6\;m/s^2$$
d. The total energy is the PE at maximum distance from equilibrium.
$$E=0.5kA^2=0.5(184\;N/m)(0.1567\;m)^2=2.26\;J$$
e. Mechanical energy is conserved. First find the PE at that position.
$$PE=0.5k(0.40A)^2=0.5(184\;N/m)((0.40)(0.1567\;m)^2=0.361\;J$$
The KE is the total energy minus that quantity.
$$2.26\;J-0.361\;J=1.90\;J$$