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.
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!