A is the answer of course
Answer:

Explanation:
We have given mass m=0.155 kg
Force constant K = 305 N/m
Distance 
Velocity 
The total energy at any position of the motion is give by
here
is energy due to motion and
is energy due to spring elongation
So total energy 
Answer:
Explanation:
We will use the KE equation you wrote here and fill in what we are given:
and isolating the m:
which gives us
m = .50 kg
Answer:

Explanation:
First we need to state our assumptions:
Thermal properties of ice and water are constant, heat transfer to the glass is negligible, Heat of ice 
Mass of water,
.
Energy balance for the ice-water system is defined as

a.The mass of ice at
is defined as:
![[mc(0-T_1)+mh_i_f+mc(T_2-0)]_i_c_e+[mc(T_2-T_1)]_w=0\\\\m_i_c_e[0+333.7+418\times(5-0)]+0.3\times4.18\times(5-20)=0\\m_i_c_e=0.0546Kg=54.6g](https://tex.z-dn.net/?f=%5Bmc%280-T_1%29%2Bmh_i_f%2Bmc%28T_2-0%29%5D_i_c_e%2B%5Bmc%28T_2-T_1%29%5D_w%3D0%5C%5C%5C%5Cm_i_c_e%5B0%2B333.7%2B418%5Ctimes%285-0%29%5D%2B0.3%5Ctimes4.18%5Ctimes%285-20%29%3D0%5C%5Cm_i_c_e%3D0.0546Kg%3D54.6g)
b.Mass of ice at
is defined as:
![[mc(0-T_1)+mh_i_f+mc(T_2-0)]_i_c_e+[mc(T_2-T_1)]_w=0\\\\m_i_c_e[2.11\times(0-(20))+333.7+4.18\times(5-0)]+0.3\times4.18\times(5-20)=0\\\\m_i_c_e=0.0487Kg=48.7g](https://tex.z-dn.net/?f=%5Bmc%280-T_1%29%2Bmh_i_f%2Bmc%28T_2-0%29%5D_i_c_e%2B%5Bmc%28T_2-T_1%29%5D_w%3D0%5C%5C%5C%5Cm_i_c_e%5B2.11%5Ctimes%280-%2820%29%29%2B333.7%2B4.18%5Ctimes%285-0%29%5D%2B0.3%5Ctimes4.18%5Ctimes%285-20%29%3D0%5C%5C%5C%5Cm_i_c_e%3D0.0487Kg%3D48.7g)
c.Mass of cooled water at 

![[mc(T_2-T_1)]_c_w+[mc(T_2-T_1)]_w=0\\m_c_w\times4.18\times(5-0)+0.3\times4.18\times(5-20)\\m_c_w=0.9kg=900g](https://tex.z-dn.net/?f=%5Bmc%28T_2-T_1%29%5D_c_w%2B%5Bmc%28T_2-T_1%29%5D_w%3D0%5C%5Cm_c_w%5Ctimes4.18%5Ctimes%285-0%29%2B0.3%5Ctimes4.18%5Ctimes%285-20%29%5C%5Cm_c_w%3D0.9kg%3D900g)