Respuesta :
Answer:
a) d^2x/dt^2 = -1.4 * x
b) x = -1.4 * cos1.2*t
Explanation:
a)
In the equilibrium state, the force of gravity like stretching equals each other:
m*g = -k*x
Being the mass of the brick of 4 kg, which causes a 7 cm stretch being in balance:
4*9.8 = -k * (-7)
39.2 = 7*k
k = 5.6
movement of the mass that is attached to the spring is equal to:
d^2x / dt^2 = -w^2 * x, where w^2 = k/m = 1.4
the differential equation is as follows:
d^2x/dt^2 = -1.4 * x
When t = 0, the rope is stretched 1.4 cm, therefore, the initial condition is equal to:
x(0) = -1.4 and x´(0) = 0
b) to solve the differential equation is equal to:
x = C1 * cos(w*t) + C2 * sin(w*t)
replacing the value of w, w = (1.4)^1/2 = 1.2
when t = 0
-1.4 = C1 * cos0 + C2 * sin0
C1 = -1.4
x´(0) = -1.2 * C1 * sin0 + 1.2 * C2 * cos0
0 = 2.2 * C2
C2 = 0
The solution to the equation is equal to:
x = -1.4 * cos1.2*t
