A mass m is attached to the end of a spring (constant k). The mass is given an initial displacement x0 from equilibrium, and an initial speed v0. Ignoring friction and the mass of the spring, use energy methods to find the following in terms of the given quantities. (Use x_0 for x0, v_0 for v0, and m, and k as necessary.)

Question

(a) its maximum speed
(b) its maximum stretch from equilibrium

Answer 1

Initial energy: 1/2 k xo + 1/2 mv^o^2

That will in all cases be the maximum total energy. So the KE will be max when spring energy is zero.

a) 1/2 m vmax^2=initial energy. solve for vmax
b)max stretch occurs when
1/2 k xmax^2=intialenergy.

Answer 2

IT DIDN'T WORK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!