Answer:
The velocity is [tex]v_x = 0.356 \ m/s[/tex]
Explanation:
From the question we are told that
The mass is [tex]m = 1.10 \ kg[/tex]
The spring constant is [tex]k = 18 \ N/m[/tex]
The speed is [tex]v = 40 \ cm / s = 0.4 m/s[/tex]
The position considered is x = 0.45 A
Here A is the amplitude which is mathematically represented as
[tex]A = v * \sqrt{\frac{m}{k} }[/tex]
=> [tex]A = 0.4 * \sqrt{\frac{1.10}{18 } }[/tex]
=> [tex]A = 0.0989 \ m[/tex]
So [tex]x = 0.45 * 0.0989[/tex]
=> [tex]x = 0.045 \ m[/tex]
Generally the speed at x is mathematically represented as
[tex]v_x = \sqrt{ \frac{k}{m} * [A^2 - x^2 ]}[/tex]
=> [tex]v_x = \sqrt{ \frac{18}{ 1.10} * [0.0989^2 - 0.045^2 ]}[/tex]
=> [tex]v_x = 0.356 \ m/s[/tex]
