A block $($with mass $\backslash ($ M $\backslash ))$ is placed on a horizontal smooth surface. A spring $($with spring constant $\backslash ($ k$=3\mathrm{.}6\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ))$ is connected to the block on one end, and a fixed wall on the other end.

$($i$)$ The block is "kicked" slightly towards the wall, so that it moves back and fro. The oscillation period is $\backslash ($ T$=4\mathrm{.}7\backslash$mathrm$\{$sec$\}\backslash ).$ What is the mass of the block?

$($ii$)$ The initial kick leads to an initial speed of $\backslash ($ v$\_\{0\}=0\mathrm{.}19\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ What is the amplitude of the oscillation?

$($iii$)$ While air resistance is small, it is not negligible. Sketch a diagram to show how the displacement of the mass changes over time. $($Mark horizontal and vertical axis to show the period and amplitude.$)$

$($iv$)$ Set up another spring and fixed wall on the other side. Again set the block into horizontal oscillation motion. What is the new oscillation period?