Total energy oscillation problem

AI Thread Summary
The displacement of a mass m = 0.01 kg is given by x(t) = 0.25m sin(62.83t/s − 0.785398), where the amplitude is determined to be 0.25 m. To find the speed at t = 0, the derivative of the displacement function is used, resulting in v(0) = (0.25)(62.83)cos(-0.785398). The total energy is expressed as the sum of kinetic and potential energy, with the formula for total energy being Total energy = (1/2)kA^2. Further clarification is needed on calculating the total energy based on the given parameters.
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Homework Statement



The displacement of a mass m = 0.01 kg is x(t) = 0.25m sin(62.83t/s − 0.785398) Find its amplitude, its total
energy, and its speed at t = 0.



Homework Equations



E = Av^2 + Bx^2
x = Asin(wt-theta)


The Attempt at a Solution



i use that above formula to find that Amplitude = .25
speed at t = 0 should be the derivative of the x function i think

v(t) = (.25m)(62.83)cos(62.83t/s - 0.785398)
v(0) = (.25m)(62.83)cos(- 0.785398)

I am not sure about the last part there with finding the energy, any suggestions?
 
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Total energy = KE + PE

Total energy = (1/2)kA2
 
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