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## Homework Statement

A particle of mass 0.50 kg performs simple harmonic motion along the x axis with amplitude 0.55m and period 4.3 seconds. The initial displacement of the particle is -0.30 m and it is travelling in the positive x-direction. The phase constant of the motion (Φ) = -2.15 rad. Find the time at which the particle first reaches x = +0.3m.

Relevant equations:

## Homework Equations

x(t) = Acos(ωt + Φ)

f = 1/T = 0.2326 Hz

ω = 2πf = 1.4612 rad/s

## The Attempt at a Solution

Rearrange for t:

t = [arccos(x/A) - Φ]/ω

t = [arccos(0.6/0.55) + 2.15]/1.4612

This is giving me a maths error because arccos(x > 1) does't exist, but 0.6m is the total displacement.

Even when I use 0.3 as my measurement for x I get a ridiculous value for t:

t = [arccos(0.3/0.55) + 2.15]/1.4612

t = 40.4423 s

Not sure where I'm going wrong. Any help would be great!