Simple Harmonic Motion of a machine part problem

Homework Statement

A machine part is undergoing SHM with a frequency of 5 Hz and an amplitude of 1.8 cm. How long does it take the part to go from x=0 to x=-1.80 cm ?

Homework Equations

x = Acos (ωt + φ)

The Attempt at a Solution

1.80 cm = 1.80 cm * cos (ωt + φ)
ω = 2πf = 2π* 5hz

cos (ωt + φ) = 1

ωt + φ = 2π

What would φ be?

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The phase φ in simple harmonic motion is basically your choice of time origin, i.e. it tells you what the displacement and velocities are at t = 0.

For example, at t=0, if you started the motion at x = -A, you would get φ = π. If your initial condition was x = 0, you have φ = +/- π/2. (Whether it is plus or minus depends on which direction you are moving at t = 0). And so on.

Back to this problem, choose an initial condition of your liking (it does not matter what you choose, you can always choose an arbitrary time origin). Then you can work out what φ is.

Hint: There is an easier way to do this problem, by symmetry considerations.

Unfortunately, I don't know what you mean by symmetry conditions. However, I think I understand what you said. I came up with an answer of .05 seconds.

Thanks for your help!

Last edited:
LowlyPion
Homework Helper
Isn't the question really how long does it take for a sinusoidal to go from the zero crossing to maximum negative amplitude?

What part of a cycle is that? How long would that be then?