An object is attached to a horizontal spring. It is initially displaced by distance Δx from the equilibrium position and then released from rest. When the object passes the equilibrium position, its speed will be:
a)v = 0 m/s
b)v proportional to Δx (the speed is proportional to the initial displaceent)
c)v proportional to Δx2 (speed is proportional to the square of the initial displacement)
d)v is a non-linear function of the Δx, but cannot be written in the form "v proportional to Δx2"
My ans:
I know that a springs equilibrium position is obtained by:
Ee = 1 / 2kx^2
and elastic potential energy is related to kinetic energy via Ee=-Ek
So I solve for k in the elastic potential energy and find out how the velocity is related? I think the answer is a, but i m not sure