Question #123783

A particle performs a simple harmonic motion about a point x=0m, with amplitude 0.5m and frequency 4Hz. Given that it is momentarily at rest at x=0.5m with t=0s. Determine, the time required for the particle to move from point x=0 to a point 0.3m away.

Expert's answer

"y=A\\cos(\\omega t+\\phi)"

"t=0 \\to y=0.5"

So,

"\\phi=0"

"y=0.5\\cos(2\\pi\\nu t)=0.5\\cos(8\\pi t)"

If "y=0" then "t_0=1\/16s=0.037s"

If "y=0.3" then "t=\\frac{1}{8\\pi}\\cos^{-1}(0.6)=0.0625s"

Finally

"\\Delta t=0.0625-0.037=0.0255s"

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