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a mass of 0.5 kg is attached to a spring and set into oscillation on a...

a mass of 0.5 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. the simple harmonic motion of the mass is described by x(t)= (0.5m)cos[(18 rad/s) t]. Determine the following:

a. position of the mass after it has been oscillating for one half a period

b. position of the mass one-third of a period after it has been released

c. the time it takes to get to the position x= -0.1m after it has been released

please explain in DETAIL (diagrams, derivation of equations, and algebra) how to arrive at the answers.

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