Ask Your Teacher A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 8 m/s. Find the equation of motion.

-(4 sin2t)

Explanation:

Let m = mass attached

k = spring constant

Using newton's second law of motion,

Md²x/dt² = -kx

where x(t) = displacement from equilibrium position.

d²x/dt² + (k/m)*x = 0

Using Hooke's law,

W = Ks

K = w/s = 640/4 = 160N/m

Put m = 40kg and k = 160N/m

d²x/dt² + (160/40)x = 0

d²x/dt² + 4x = 0

Note: w = k/m = 160/40 = 4 rad/s

x¹¹ + ω²x = 0

the general solution is,

x(t) = c₁ cos2t + c₂sin2t

Using the conditions

x(0) = 0ft

x¹(0) = -8m/s

x(t) = -4sin2t