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kgal
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Homework Statement
A massive object of m = 5.2 kg oscillates with simple harmonic motion. Its position as a function of time varies according to the equation x(t) = 1.6sin(∏t/1.6 + ∏/6).
a. What is the position, velocity and acceleration of the object at t = 0s?
b. What is the kinetic energy of the object as a function of time?
c. At what time after t=0s is the kinetic energy first at a maximum?
Homework Equations
x(t) = 1.6sin(∏t/1.6 + ∏/6).
The Attempt at a Solution
a. x(0) = 1.6sin(0 + ∏/6) = 0.8 m
v(0) = ∏cos[(∏t / 1.6) + (∏/6)] = ∏cos(∏/6) = 2.72 m/s
a(0) = - (∏^2 / 1.6) sin [(∏t / 1.6) + (∏/6)] = - 5.33 m/s^2 (the right answer should be -3.08 m/s^2)!
b. K(t) = 1/2mv(t)^2 = 1/2m{[∏cos[(∏t / 1.6) + (∏/6)]}^2 //plugged v from part a
2.6∏^2cos^2[(∏t / 1.6) + (∏/6)]
c. K' = -100sin[(∏t / 1.6) + (∏/6)]cos[(∏t / 1.6) + (∏/6)].
K'(t) = 0 at t = .26 s (But the right answer should be 1.33 s)!