A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 7 cm. The spring is then stretched an additional 2 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g

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

they should be similar or the same

neither accurate nor precise.