A block of mass m is attached to a spring with spring constant k and is observed to execute damped harmonic motion (no driving force) with its position x given by

x=Ae??tcos(?t+?),

with ?=7.0 s?1 and ?=27.0 s?1. Note that ?=b/2m.

(a) If the mass of the block is 4.13 kg find the value of the spring constant k.

____N/m

(b) The block and spring are now changed to m=0.5 kg and k=389 N/m with the damping the same as in part (a). The block is now driven with a force given by

F=(1.25N)cos(?t+?)

with ?= 31.79 s?1 Find the amplitude of the block in meters after the force has been driving the block for several minutes.

____m