A mass m = 3.4 kg is at the end of a horizontal spring of spring constant k = 105 N/m on a frictionless horizontal surface. The block is pulled, stretching the spring a distance A = 6.5 cm from equilibrium, and released from rest.
(a) Write an equation for the angular frequency of the oscillation
(b) Calculate the angular frequency o of the oscillation in rad/seconds

b.

Explanation:

a. from the spring-mass system which is explicitly describe by hooks law

from

F=-kx

which is in comparison to newtons general law of motion

F=ma

where the displacement x is expressed as

and the acceleration is the second derivative of the displacement

hence final expression after substituting for the acceleration and the displacement  is expressed as

b. for k=105N/m and m=3.4kg

we have the angular frequency to be

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.