# # In order to reduce the damaging effects of rapid speed changes, a manual transmission contains a set of coiled springs on the outer edge of the plate. A simplistic version of a clutch plate is shown in the diagram above. When shifting gears, the springs are compressed. This helps reduce vibrations and make shifting smooth. At the end of each of these springs exists a block, $$m = {{ params.m }}kg$$ on which the force acts. The springs are $$d = {{ params.d }}mm$$ from the centre, and have a stiffness of $${{ params.k }}N/m$$. The end of the spring starts with a distance of $$x_0 = {{ params.x }}mm$$ from the center, perpendicular to $$d$$. Answer the following questions with the given information. Neglect friction and the mass of the springs.

## Part 1#

If the clutch spins at $$\omega= {{ params.w }}rev/min$$, determine the value of $$x$$, the final distance of the blocks on the end of the spring.

Please enter in a numeric value in metres.

## Part 2#

Find the normal force $$N$$ exerted by the side of the slot on the block.

Please enter in a numeric value in Newtons.

## Part 3#

What force would be needed to compress the springs below the resting point by $$\Delta x = {{ params.d2 }}$$? 