A mass is oscillating on a spring with a period of 4.60 s. At t=0 s, the mass has zero speed and is at x=8.30 cm.  a) What is the value of t the first time after t=0 s that the mass is at x=4.15...

A mass is oscillating on a spring with a period of 4.60 s. At t=0 s, the mass has zero speed and is at x=8.30 cm. 

a) What is the value of t the first time after t=0 s that the mass is at x=4.15 cm?

b) What is its acceleration at t= 2.50 s ?

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Naomi Little eNotes educator | Certified Educator

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First, we'll start by deriving the equation that describes the motion of the spring. Considering we only have a spring and mass without a damper, the equation is simple:

`x(t) = Acos(omegat- phi)+c`

We will use cosine because we start at the maximum displacement without having to worry about phase shift or vertical shift. A can be derived from the maximum displacement,...

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