- #1

- 199

- 0

## Homework Statement

A particle moves with simple harmonic motion of period [tex] \frac{\pi}{2} [/tex]. Initially it is 8cm from the centre of motion and moving away from the centre with a speed of [tex] 4 \sqrt{2} [/tex] cm/s.

Find an equation for the position of the particle in time t second.

## Homework Equations

[tex] x = A \cos{ \omega t + \epsilon} [/tex]

[tex] v^2 = \omega^2 (A^2 - x^2) [/tex]

[tex] T = \frac{2 \pi}{\omega} [/tex]

## The Attempt at a Solution

[tex] T = \frac{2 \pi}{\omega} [/tex]

[tex] \omega = 4 rad s^-1 [/tex]

[tex] v^2 = \omega^2 (A^2 - x^2) [/tex]

[tex] 32 = 16(A^2 - 64) [/tex]

[tex] A = \sqrt{66} [/tex]

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

[tex] x = \sqrt{66}\cos(4t + \epsilon) [/tex]

The answer in the book is:

[tex] x = \sqrt{66}\cos(4t + .175) [/tex]

I don't understand where the .175 comes from.

Thanks for any help.