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This question is based on Oscillations and waves. I tried it for days and I just couldn't get it right.

This Question Is Based On Oscillations And Waves I Tried It For Days And I Just Couldnt Get It Right class=

Sagot :

ANSWER:

The maximun velocity is 16.07 m/s

At x = 0.26

The velocity is 8.36 m/s

The accelearion is 286.67 m/s^2

The resorting force is 86 N

STEP-BY-STEP EXPLANATION:

Given:

k = 310 N / m

Max distance = 0.5 m

Mass of block = 0.3 kg

Max velocity:

Using conservation of energy:

[tex]\begin{gathered} \frac{1}{2}kx^2=\frac{1}{2}mv^2 \\ v^2=\frac{kx^2}{m} \\ \text{ replacing} \\ v^2=\frac{310\cdot0.5^2}{0.3} \\ v=\sqrt[]{258.33} \\ v=16.07\text{ m/s} \end{gathered}[/tex]

At x = 0.26 m:

[tex]\begin{gathered} v^2=\frac{kx^2}{m} \\ v^2=\frac{310\cdot0.26^2}{0.3} \\ v=\sqrt[]{69.85} \\ v=8.36\text{ m/s} \end{gathered}[/tex]

Acceleration:

[tex]\begin{gathered} F=k\cdot x \\ F=m\cdot a \\ \text{ therefore} \\ m\cdot a=k\cdot x \\ a=\frac{k\cdot x}{m} \\ \text{ replacing} \\ a=\frac{310\cdot0.26}{0.3} \\ a=286.67\text{ }\frac{m}{s^2} \end{gathered}[/tex]

The resorting force:

[tex]\begin{gathered} F=m\cdot a \\ \text{ replacing} \\ F=0.3\cdot286.67 \\ F=86\text{ N} \end{gathered}[/tex]

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