You attach one end of a spring with a force constant

Question

k = 893 N/m
to a wall and the other end to a mass
m = 2.02 kg
and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position
xi = 6.56 cm
from equilibrium and release it.

a) Determine the potential energy stored in the spring before the block is released.

(b) Determine the speed of the block as it passes through the equilibrium position.

(c) Determine the speed of the block when it is at a position
xi/4.

Answer 1

a) The potential energy stored in the spring before the block is released is U = 1/2 kx^2 = 1/2 (893 N/m)(0.0656 m)^2 = 3.7 J.

b) The speed of the block as it passes through the equilibrium position is v = sqrt(2U/m) = sqrt(2(3.7 J)/(2.02 kg)) = 1.6 m/s.

c) The speed of the block when it is at a position xi/4 is v = sqrt(2U/m) = sqrt(2(3.7 J)/(2.02 kg)) = 1.6 m/s.