Answer :
The formula for total mechanical energy at maximum displacement (amplitude) is
ME = KE + PE = 0 plus (1/2)
*k*A^2 = (1/2)*k*A^2
Now, mechanical energy is constant during the displacement of a mass on a spring.
Now, when x equals A/2, or when displacement is equal to half of amplitude, then
PE = (1/4)*(1/2)*k*x2 = (1/4)*(1/2)*k*(A/2)*2
PE = (1/4)*ME
PE = ME - (1/4)*ME - KE = ME
KE = (3/4)*ME
KE/ME = 3/4 = 0.75
Part B.
When KE = PE, displacement is required.
If this event happens at 'x' displacement, then at this point we are aware that
ME = KE plus PE equals (1/2)*k*A2.
Because KE = PE
ME = PE + PE = (2*PE)*k*A2
PE = (1/4)*k*A^2
PE = (1/2)*k*x2 at x displacement, thus
(1/2)*k*x^2 = (1/4)*k*A^2
x^2 = (1/2)*A^2
(x/A)^2 = 1/2
sqrt(1/2) = 0.7071 for x/A
Using two reliable figures
x/A = 0.71
Click the following link to learn more about kinetic energy:
https://brainly.com/question/9206084
#SPJ4
