Answer:
y = 1 cos 10t inch
Explanation:
This exercise creates a simple harmonic motion, which is described by the equation.
y = A cos (wt + φ)
The initial load of 1 lb creates a new equilibrium point (y₀), but does not intervene in the movement because it is in equilibrium, the unbalanced force is created by the movement.
The system lengthens 1 inch. Additional this is the breadth
A = 1 in
The angular velocity is given by
w = √ (k / m)
w = √ (100/1)
w = 10 rad / s
The angle φ is determined by the initial conditions
In this case for maximum elongation is released, the speed is zero at this point
v =dy/dt = - A w sin (wt + φ)
0 = A w sin(w 0 + φ)
0 = sin fi
fi = 0
With these results we can write the equation
y = 1 cos (10 t +0)
y = 1 cos 10t inch
