physics help?

Question

at t=0 a .755kg mass at rest on the end of a horizontal spring (k=124N/m) is struck by a hammer which gives the mass an inital speed of 2.96m/s determine the postion as a function of time and find the total energy

Answer 1

Kinetic energy (Ke) = Initial energy = final energy (if no friction and othe rlosses)

Ke= 0.5 mV^2

x(t)= A sin(wt +ph)

We can find A by using the relationship between kinetic and potential energy of oa compressed string
Ke= Ps= 0.5kA^2

0.5 mV^2= 0.5kA^2
A= mV^2/k
and
w= sqrt(k/m)