Aspring is hung from the ceiling. a 0.473 -kg block is then attached to the free end of the spring. when released from rest, the block drops 0.109 m before momentarily coming to rest, after which it moves back upward. (a) what is the spring constant of the spring? (b) find the angular frequency of the block's vibrations.

a)

85.05 N/m

b)

179.81 rad/s

Explanation:

a)

k = spring constant of the spring

m = mass of the block = 0.473 kg

x = stretch caused in the spring = 0.109 m

h = height dropped by the block = 0.109 m

Using conservation of energy

Spring potential energy gained by the spring = Potential energy lost by the block

(0.5) k x² = mgh

(0.5) k x² = mgx

(0.5) k x = mg

(0.5) k (0.109) = (0.473) (9.8)

k = 85.05 N/m

b)

angular frequency is given as

= 179.81 rad/s

real, smaller and upside-down.   so the answer should be b.