# Thread: [SOLVED] 2 model springs

1. ## [SOLVED] 2 model springs

Now that an extra model spring is attached, as shown, what will the vector force due to the additional spring be? Can someone explain why the equation of motion is

mx+5kx=-mgsin(alpha) +11kl0

2. Hi ithink I can work out the rest of teh question if someone can tell me how to use hookes law for 2 springs.

Is this just -3k(5l0-x-l0) = -3k(4l0-x). Note the l0 stands for L with a little 0 at the bottom (i.e. initial)

3. If I was going to chose a datum for the gravitational potential energy of the particle, would the block P be the best choice? And would it point directly downwards towards W?

4. Originally Posted by moolimanj
Now that an extra model spring is attached, as shown, what will the vector force due to the additional spring be? Can someone explain why the equation of motion is

mx+5kx=-mgsin(alpha) +11kl0
There is a weight on the block directed downward, there is a normal force on the block directed out of the plane of the slope, there is a spring force acting down the incline and a spring force acting up the incline.

The spring extension of the lower spring is presumably $x - l_0$? Since the top spring has an equilibrium length of $2l_0$, the spring extension of the upper spring is $(5l_0 - 2l_0) - x$. So Newton's 2nd tells us
$\sum F_x = -mg~sin(\alpha) + 3k(3l_0 - x) - 2k(x - l_0) = ma$

This gives the required equation of motion.

-Dan

5. Originally Posted by moolimanj
If I was going to chose a datum for the gravitational potential energy of the particle, would the block P be the best choice? And would it point directly downwards towards W?
This is confusing. What are you trying to ask? What is a good reference level to set the gravitational potential energy to 0 J at? What direction is W? It's not on your diagram.

-Dan

6. How do I determine the general and particular solution of the differential equation:

mx+5kx=-mgsin(alpha)+11kl0

note the x variable in mx has two dots on the top of it.

What is the period and amplitude and what would teh graph look like

7. Ive just answered this question so it can be removed from urgent homework help