Question

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?

Answer 1

`= (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"`