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danago
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A particle moves in a straight line so that its position, x cm, from a fixed point O, at time t seconds is given by x=3+12sin(2\pi t)+5cos(2 \pi t).
Prove that the particle is undergoing simple harmonic motion, and find x when its speed is 26\pi cm/s.
I was fine with the first part of the question...
<br /> \begin{array}{l}<br /> x = 3 + 12\sin (2\pi t) + 5\cos (2\pi t) \\ <br /> v = \dot x = 24\pi \cos (2\pi t) - 10\pi \sin (2\pi t) \\ <br /> a = \ddot x = - 48\pi ^2 \sin (2\pi t) - 20\pi ^2 \cos (2\pi t) = - 4\pi ^2 (x - 3) = 12\pi ^2 - 4\pi ^2 x \\ <br /> \end{array}<br />
With the second part, i can easily set the velocity equal to 26\pi and solve it on my calculator, but how can i solve it algebraically?
Thanks in advance,
Dan.
Prove that the particle is undergoing simple harmonic motion, and find x when its speed is 26\pi cm/s.
I was fine with the first part of the question...
<br /> \begin{array}{l}<br /> x = 3 + 12\sin (2\pi t) + 5\cos (2\pi t) \\ <br /> v = \dot x = 24\pi \cos (2\pi t) - 10\pi \sin (2\pi t) \\ <br /> a = \ddot x = - 48\pi ^2 \sin (2\pi t) - 20\pi ^2 \cos (2\pi t) = - 4\pi ^2 (x - 3) = 12\pi ^2 - 4\pi ^2 x \\ <br /> \end{array}<br />
With the second part, i can easily set the velocity equal to 26\pi and solve it on my calculator, but how can i solve it algebraically?
Thanks in advance,
Dan.
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