Answer:
Explanation:
Given that:
angular frequency = 11.3 rad/s
Spring constant (k) = [tex]= \omega^2 \times m[/tex]
k = (11.3)² m
k = 127.7 m
where;
[tex]x_1[/tex] = 0.065 m
[tex]x_2[/tex] = 0.048 m
According to the conservation of energies;
[tex]E_1=E_2[/tex]
∴
[tex]\Big(\dfrac{1}{2} \Big) kx_1^2 =\Big(\dfrac{1}{2} \Big) mv_2^2 + \Big(\dfrac{1}{2} \Big) kx_2^2[/tex]
[tex]kx_1^2 = mv_2^2 + kx_2^2[/tex]
[tex](127.7 \ m) \times 0.065^2 = v_2^2 + (127.7 \ m) \times 0.048^2[/tex]
[tex]0.5395325 = v_2^2 +0.2942208 \\ \\ 0.5395325 - 0.2942208 = v_2^2 \\ \\ v_2^2 = 0.2453117 \\ \\ v_2 = \sqrt{0.2453117} \\ \\ \mathbf{ v_2 \simeq0.50 \ m/s}[/tex]