{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT2_017JF09_p15

# MIT2_017JF09_p15 - 15 BOUNCING ROBOT 15 37 Bouncing Robot...

This preview shows pages 1–2. Sign up to view the full content.

15 BOUNCING ROBOT 37 15 Bouncing Robot You are asked to explore the simple dynamics of a bouncing robot device, using simulation. There is a single mass with a very light helical spring attached on the bottom of it; the mass is 40 kg , and the spring constant is 10400 N/m . The spring additionally has a little bit of damping, 35 Ns/m . The spring is NOT attached to the ground. The initial condition has zero vertical velocity and a 15 cm compression of the spring. 1. Formulate the system dynamics with an annotated drawing and a statement of the governing equations. Solution: Let us say that vertical position y = 0 corresponds with the spring in its natural, uncompressed state, and it is just touching the ground. Then when y < 0 , there is a compression force pushing the mass upward at ky , and the associated damping by ˙ . When y > 0 , there is no spring force at all. In all cases, there is a steady gravity force acting. We have then: my ¨ + by ˙ + ky = mg when y < 0 , or my ¨ = mg when y > 0 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}