I am stumped on this homework problem and would like help at least to get me thinking in the right direction: It is a 2-D problem where a spring "plunger" is being used to propel a block forward. More specifically: the block rests against an ideal spring that is being held in a compressed state. Once the spring is released from its compressed state, the force produced by that ideal spring as it expands propels the block across a frictionless surface.

Question

I am stumped on this homework problem and would like help at least to get me thinking in the right direction: It is a 2-D problem where a spring "plunger" is being used to propel a block forward. More specifically: the block rests against an ideal spring that is being held in a compressed state. Once the spring is released from its compressed state, the force produced by that ideal spring as it expands propels the block across a frictionless surface. 
     If I am given the mass of the block, the spring constant constant k and the distance by which the spring is held compressed before being released, how could I find the initial velocity of the block after it leaves the spring?  
     Thank you for any help you may be able to provide.

Anonymous · Answer

force of spring = -kx = m x a m d2/d2t(x) + kx = 0 solve this differential equation for x(t)