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Classical Mechanics

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Acceleration of a Harmonic Oscillator

CLMECH-GHU6XY

We can model the up and down motion of a piston in an engine as a harmonic oscillator with its position described by:

$$y(t) = \frac{d}{2}\sin(2\pi f t)$$

...where $f$ is the oscillation frequency (in units of 1/sec) and $d$ is the total distance from the bottom of its motion to the top.

What is the acceleration of this piston (mark ALL that apply)?

A

$a =\cfrac{d^2 y}{dt^2}$

B

$a =\cfrac{\Sigma F}{m}$

C

$a =\pi f d \cos(2\pi ft)$

D

$ a = -2 d (\pi f)^2 \sin(2\pi f t)$

E

$a = \cfrac{\Delta v}{\Delta t}$