Can you write a matlab code for this?? The vertical position of a mass on a spring oscillates after being released if it is not initially at equilibrium, but the amplitude of the oscillation decreases exponentially $($due to air resistance$).$

Assume that for a particular mass$-$spring system, the vertical position y of the mass follows y$=$e$^-$t cos$(2$pir$),$ where t is time. In this case, the vertical velocity of the mass is v$=-$e$^-$t $(2$pisin$(2$pit$)+$cos$(2$pit$)).$

Write a MATLAB script in which you: Create a time vector t of equally spaced values between $0$ and $5,$ in increments of $0\mathrm{.}01.$

Calculate the vertical position y for every time value.

Calculate the vertical velocity v for every time value.

On the left y$-$axis, plot the vertical position versus time.

Set the left y$-$axis limits to $-1$ and $1.$

Label the left y$-$axis $"$y$".$

On the same figure, but on the right y$-$axis, plot the vertical velocity versus time.

Set the right y$-$axis limits to $-6$ and $6.$

Label the right y$-$axis $"$v$".$

Label the x$-$axis $"$t$".$

Title the axes "Vertical position and velocity over time".