Twin spring system with a mass in between (X and Y direction)

[BvU]

If the mass moves 1 unit of length in the +x direction, what is the change in $L_1$ ? And in $L_2$ ? This has consequences for $F_1, F_{1,x}, F_{1,y}, \theta_1, F_2, F_{2,x}, F_{2,y}, F_{tot, x}, F_{tot, y}, \theta_2$ so also for $a_x, a_y$

[edit] and $\sin\theta_1 = h/L_1 \quad \Rightarrow \quad \theta_1 = \arcsin (h/L_1)$, etc !

 

[BvU]

The simulation you are setting up will integrate the equations of motion, $\vec {\bf a} = \vec {\bf F} / m$

At $t_0 = 0$ you have $$ x_0 = 0, \\ y_0= 0, \\ v_{x,0} = ..., \\ v_{y,0} = ... , \\ a_{x,0} = 0, \\ a_{y,0} = 0
$$With the simplest integrator, forward Euler, you can calculate the situation
at t = $t_0 + \Delta t$:$$ x = x_0 + v_{x_0} \Delta t , \\ y = y_0 + v_{y,0} \Delta t, \\ v_{x} = v_{x_0} + a_{x,0} \Delta t \\
v_{y} = v_{y_0} + a_{y,0} \Delta t
$$ and then you need to calculate a new $\vec {\bf a}$ at position $\left (x(\Delta_t), y(\Delta_t) \right )$
and so on.

 

[MrNewton]

The simulation you are setting up will integrate the equations of motion, $\vec {\bf a} = \vec {\bf F} / m$

For some reason i cannot reply your equation without the site going nuts.

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Thanks for those equations. THIS ONE, : X = X₀ + V₀ * ΔT, Shouldtn it be, X_n = X_n-1 + V_n * ΔT ?
With n the current timestep
So the current speed instead of the previous speed?

and for the acceleration:, a_n+1 = F_n+1/m

 

[haruspex]

Thanks for those equations. THIS ONE, : X = X₀ + V₀ * ΔT, Shouldtn it be, X_n = X_n-1 + V_n * ΔT ?
With n the current timestep
So the current speed instead of the previous speed?

and for the acceleration:, a_n+1 = F_n+1/m

The starting point is the position and velocity, $\vec r_0$, $\dot{\vec r}_0$.
From these you calculate an acceleration, $\ddot {\vec r}_0$.
For the next timestep, $\dot {\vec r}_1=\dot{\vec r}_0+\ddot {\vec r}_0\Delta t$.
So for calculating $\vec r_1$ you have two velocities available. Taking the average should work well.