Tom travels to the moon for NASA. While on the moon, the total weight of Tom and his lunar exploration suit is 224 N. His suit h
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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: