Pendulum Hits a Mass and Spring I think this problem’s solution is on the web but after a few days of searching, I can not find it. Can anyone give me a reference? Thanks in advance.
A mass and spring are resting on a frictionless table. A pendulum is pulled back, released, and hits the mass.  The spring coils, recoils, and propels the pendulum. 
One of the interesting aspects of this problem is the driving force appears then disappears every now and then. How is this modeled.
Thanks in advance.
 A: 1 - Calculate potential energy of the pendulum.
2 - Hypotesis: perfectly elastic bodies => All the pendulum energy is transfered to the resting mass and spring.
3 - When all the energy is stored into the spring calculate x as the position of the mass using the formula of the potential energy of a spring.
4 - Finally the energy released from the spring passes to the pe
ndulum which returns to the initial position.
A: If the pendulum of mass $m_1$ (with length $\ell$) hits the elastically supported mass $m_2$ (with spring $k$) then an impulse $J$ is going to slow the pendulum and accelerate the spring.
Before the impact the speeds are $v_1=0$, $v_2=v_{impact}$ and after $v_1+\frac{J}{m_1}$ and $v_2-\frac{J}{m_2}$.
The elastic collision will return a portion of the impact speed given a coefficient of restitution $\epsilon$ such that
$$ \left(v_1+\frac{J}{m_1}\right) - \left( v_2-\frac{J}{m_2} \right) = -\epsilon \left( v_1 - v_2 \right) $$
The above is solved for the impulse as
$$ \boxed { J = \frac{ (\epsilon+1) (v_2-v_1) }{ \frac{1}{m_1} + \frac{1}{m_2} } } $$
with the updated speeds $v_1 \rightarrow v_1+\frac{J}{m_1}$ and $v_2 \rightarrow v_2-\frac{J}{m_2}$
Now continue solving for the pendulum and spring motion, until the next impact.
