I need help with b... I found that k=.750880 for part a but I can't figure out what y would be to get potential energy.

A 52 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to:
y(t) = 0.8 * sin( 3.8 * t ) where y is measured in meters and t in seconds.

(a) What is the spring constant in N/m?

k = .750880 N/m

(b) What is the Total Energy in the mass and spring in J?

E = ???J

HELP: The total energy is the sum of the kinetic energy and potential energy. At what point in the motion is the energy all kinetic? At what point is it all potential? Can you compute it at this point?

HELP: Kinetic energy is 1/2 * Mass * v2

Potential energy is 1/2 * k * y2

We know that at the mass's maximum y-position it has zero velocity, so simply compute Potential Energy at that point.

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  1. At equilibrium position, K.E.=max,P.E. = 0
    At the two extreme points, K.E.=0,P.E.=max

    Total energy is constant at ANY POINT.
    We find E at extreme point.
    E = 1/2*k*(0.8)^2
    = 0.24J

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    posted by Marco
  2. but you know the velocity
    dy/dt = .8 * 3.8 cos (3.8 t)
    maximum velocity when sin (3.8 t) = 1
    max Ke = total = (1/2) (.052)(.8*3.8)^2

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    posted by Damon
  3. lol, both method can find the answer

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    posted by Marco

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