Question

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

Answer 1

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

Explanation:

Given:

k = 310 N / m

Max distance = 0.5 m

Mass of block = 0.3 kg

Max velocity:

Using conservation of energy:

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

At x = 0.26 m:

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

Acceleration:

`\begin{gathered} F=k\cdot x \\ F=m\cdot a \\ \text{ therefore} \\ m\cdot a=k\cdot x \\ a=(k\cdot x)/(m) \\ \text{ replacing} \\ a=(310\cdot0.26)/(0.3) \\ a=286.67\text{ }(m)/(s^2) \end{gathered}`

The resorting force:

`\begin{gathered} F=m\cdot a \\ \text{ replacing} \\ F=0.3\cdot286.67 \\ F=86\text{ N} \end{gathered}`