a,b, and c I want to know the steps please, especially number c. draw the graph.

Question

a,b, and c I want to know the steps please, especially number c. draw the graph. I also want to know if there are many t(s) solution and how to pick one of them. clear, step by step

thanks

9. 2/3 points | Previous Answers The motion of a mass connected to a spring is described by the equation (in SI units) x = 9 sin(3.81t + 1.047) a) What is the period of oscillation? 1.65 b) What is the positive displacement x when the kinetic energy equals the potential energy? 6.36 c) At what positive time is this condition and displacement achieved? 0.216 sec xsec

Explanation / Answer

a] comparing the equation with x = A sin (wt + phi)

here w =3.81

now period = 2pi/w = 2pi/3.81 = 1.65 s

b] maximum potential energy = 0.5 kA^2 when x = A

when potential energy = kinetic energy, potential energy will be half of its maximum,

0.5kx^2 = 0.5*0.5kA^2

x = A / sqrt 2 = 9/sqrt 2 = 6.36 m

c] clearly it will be when sin(3.81t +1.047) = 1/ sqrt2

or 3.81t + 1.047 = pi/4 or 3pi/4, pi/4 will be rejected as it will make t negative.

  3.81t + 1.047 = 3pi/4

t = [3 pi /4 - 1.047 ]/3.81

= 0.3436 sec answer

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