Answer:

Explanation:
From the information given:
The equation of the motion can be represented as:

where:
= mass of the body 1
= mass of the body 2
= acceleration
k = spring constant
u = displacement
g = acceleration due to gravity
Recall that the formula for natural frequency 
And the equation for the general solution can be represented as:

To determine the initial velocity, we have:


where h = height
Suppose we differentiate equation (2) with respect to time t; we have the following illustration:

now if t = 0
Then


Using the law of conservation of momentum on the impact;

By replacing the value of
with 
Then the above equation becomes:

Making u(0) the subject of the formula, we have:

Similarly, the value of the variable can be determined as follows;
Using boundary conditions



Also, if 
Then :

making B the subject; we have:

Finally, replacing the value of A and B back to the general solution at equation (2); we have the equation of the subsequent motion u(t) which is:
