Answer:
x = A cos wt
Explanation:
To determine the position we are going to solve Newton's second law
F = m a
Spring complies with Hooke's law
F = -k x
And the acceleration of defined by
a = d²x / dt²
We substitute
- k x = m d²x / dt²
dx² / dt² + k/m x = 0
Let's call
w² = k / m
The solution to this type of differential equation is
x = A cos (wt + Ф)
Where A is the initial block displacement and the phase angle fi is determined by or some other initial condition.
In this case the body is released so that at the initial speed it is zero
From which we derive this expression
v = dx / dt = a w sin ( wt + Ф)
As the System is released for t = 0 the speed is v = 0
v = sin Ф = 0
Therefore Ф = 0
And the equation of motion is
x = A cos wt
