Recent content by slurd

Hm... I still can't get something. So I linearise it as ##f = 2kl(1 - \frac{l}{s})\sin\theta##, then I project the weight on the same axis and say that total force is ##f + W_{projection}##, which isn't really a linear combination of ##Δx##, so not a restoring force? If I take ##\sum{\tau}=\tau...

Of course, this is where I was stuck because I'm used to different notation for unit vectors. Thanks.

Why is the force $$ \vec F = k \frac {\vec s} s (s - l) = k \left(1 - \frac l s \right) \vec s $$ ? Thanks a lot.

Well I have trouble finding the angle on which I have to project the restoring force to calculate the torque. Can I do this with the force and not torques?

Well that is puzzling... I end up with a ##θ## in the restoring force and not a displacement in length units. The Taylor series for ##\sqrt{5-4cosθ}## is ##1+θ^2-...## so that would make ##Δx_3=l(1+\frac{θ^2}{2}-1)=l\frac{θ^2}{2}## and the restoring force ##F=-kΔx_3=-kl\frac{θ^2}{2}##

Can I accept the approximation ##Δx_3=0## and claim the spring and bar will act as a pendulum?

Yes but if ##θ## is infinitesimally small, wouldn't ##θ^{2}## be even smaller, so negligible? Αlso about the ##l^4##, I'm really absent-minded and sleepless, forgive me.

Οοps, was thinking of 90 degrees. 180 is not possible, since the bar would be stopped by the floor's surface. Okay I found what was wrong with the Δx=0 equation. But now I'm at this: ##Δx_{1} = lsinθ ## ##Δx_2 = l-lcosθ ## pythagorean theorem: ##Δx_{1}^{2} +...

There will still be a component on the x-axis of the spring's hooke's law force that will point to the left, don't I need ##∑F=0## for equilibrium? I presume that it is messy because I am not doing it correctly. I can't simplify the cosθ and sinθ because the Δx ends up 0.

Homework Statement A bar with length l and homogeneous mass distribution (mass: m) can rotate around its fixed point O.The other edge of the bar is connected to the spring in the figure of constant k and length l, and the spring is fixed by its one edge at point P. The system is in the...