Given:
The spring constant of the spring is k = 200 N/m
The maximum displacement of the spring is x = 6 cm = 0.06 m
The time period is T = 0.2 s
To find the maximum restoring force and the maximum acceleration.
Explanation:
The maximum restoring force applied on the block can be calculated as
[tex]\begin{gathered} F=kx \\ =200\times0.06\text{ } \\ =\text{ 12 N} \end{gathered}[/tex]
First, we need to calculate angular frequency.
The angular frequency can be calculated as
[tex]\begin{gathered} \omega=\frac{2\pi}{T} \\ =\frac{2\times3.14}{0.2} \\ =31.4\text{ rad/s} \end{gathered}[/tex]
The maximum acceleration can be calculated as
[tex]\begin{gathered} a=x\omega^2 \\ =0.06\times(31.4)^2 \\ =59.2m/s^2 \end{gathered}[/tex]
Final Answer: The maximum restoring force is 12 N and the maximum acceleration is 59.2 m/s^2.
