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January 8th, 2017, 02:15 PM   #1
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simple harmonic motion

I have been given some questions on simple harmonic motion and i have found some relevant formulas i am just unsure as to what they represent and how to use them

the question is:

An object moving with simple harmonic motion has a frequency of 5Hz with an amplitude of 100mm determine:

- Maximum velocity
- The velocity 50mm from the equilibrium position
- The maximum acceleration
- The acceleration 50mm from the equilibrium position
- The time taken to move from the extremity of the oscillation to a distance of 50mm from the equilibrium position
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January 8th, 2017, 04:21 PM   #2
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Do these resemble your "relevant" equations?

assuming the object exhibiting SHM starts at maximum displacement at $t=0$ ...

$\omega = 2\pi \cdot f$

position ...

$x(t) = A\cos(\omega t) \implies |x_{max}|=A$

velocity ...

$v(t) = x'(t) = -A\omega\sin(\omega t) \implies |v_{max}| =A\omega$

acceleration ...

$a(t) = v'(t) = x''(t) = -A\omega^2 \cos(\omega t) \implies |a_{max}|=A\omega^2$

see what questions you can work out ...
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