A 3kg block is attached to an ideal spring with a force constant k=200N/m. The block is given an initial velocity in the positive direction of magnitude u=12m/s and no initial displacement(x.=0). (a) find the amplitude?

1 Answer
Jul 29, 2018

Answer:

#= (3 sqrt(6))/5 " m"#

Explanation:

Conservation of total Energy #E#:

#E = T + U#

  • At displacement = 0: #qquad U = 0, qquad T = T_("max")#

  • At maximum displacement: #qquad T = 0, qquad U = U_("max")#

So:

  • #U_("max")= T_("max")#

#implies 1/2 k x_("max")^2 = 1/2 m v_("max")^2#

# :. x_("max") = sqrt(m/k) v_("max") = sqrt(3/200) * 12 #

#= (3 sqrt(6))/5 " m"#