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## Homework Statement

A 0.500 kg mass attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate (a) the maximum value of its speed and acceleration, (b) the speed and acceleration when the mass is 6.00 cm from the equilibrium position, and (c) the time it takes the mass to move from x = 0 to x = 8.00 cm.

## Homework Equations

[tex]\omega = \sqrt{ k / m }[/tex]

[tex]x = A \cos(\omega t + \phi)[/tex]

## The Attempt at a Solution

Certainly, (a) is simple, and in it we determine [tex]\omega = \sqrt{8/.5} = 4[/tex], but for (b), why would we

**not**use [tex]x = 10 \cos (4 t )[/tex]?? The solution's manual uses [tex]x = 10 \sin(4 t)[/tex]. Why would I use sine in this case and how do I tell the difference?

thanks.