A particle P is moving on a straight line with S.H.M. of period pi/3 s. Its maximum speed is 5 m/s. Calculate the amplitude of the motion and the speed of P 0.2s after passing through the centre of oscillation.
T=2pi/w So w=6
5^2=6^2(a^2-0) so a=5/6 (matched with book)
The answer given in book is 1.81.
Somebody help. What did go wrong with this very simple sum?
Interesting. I've never heard of this before, but according to wikipedia, simple harmonic motion is given by:
where is displacement, is time, is amplitude, is frequency, and is phase.
We also note that period is given by:
This means that . So:
To find velocity, we take the derivative:
To find velocity extrema, we take the derivative of and set it equal to zero:
Let's plug that into our velocity function:
Since the amplitude must be a positive value, we can just say:
Now, the center of oscillation is another way of saying . So:
Let's let and :
And we plug that into our velocity function:
Then plug in :
But of course we know that speed is relative, and so the value is actually: