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# Finding time period of an oscillator watch

1. Hi guys, I'm doing A2 Physics for OCR, and I've encountered a past paper question about a trolley attached to a spring (which is attached to a vertical unmoving surface) on a smooth table that follows simple harmonic motion, which is as follows;

'Using your knowledge of Hooke's Law and Newton's second law, determine the period T of the trolley in terms of the force constant k of the spring and the mass m of the trolley.'

(w = omega)

Now, I did F = kx = ma; I then put a = w^2x into it, to obtain kx = mw^2x; I cancelled the x on both sides, and then divided by m to obtain w^2 = k/m, as in the answers.

I then square rooted both sides, flipped both sides over so that T was on top for w, and then multiplied through so that T = 2pi(sqrt(m/k)).

The answer, however, says that I should have got T = 2pi(sqrt(k/m)), which I just don't understand... can anyone see where I've gone wrong here, or are the answers wrong?
2. Maybe you wrongly solved the double fraction - if there was one?
3. (Original post by Kyta)
Hi guys, I'm doing A2 Physics for OCR, and I've encountered a past paper question about a trolley attached to a spring (which is attached to a vertical unmoving surface) on a smooth table that follows simple harmonic motion, which is as follows;

'Using your knowledge of Hooke's Law and Newton's second law, determine the period T of the trolley in terms of the force constant k of the spring and the mass m of the trolley.'

(w = omega)

Now, I did F = kx = ma; I then put a = w^2x into it, to obtain kx = mw^2x; I cancelled the x on both sides, and then divided by m to obtain w^2 = k/m, as in the answers.

I then square rooted both sides, flipped both sides over so that T was on top for w, and then multiplied through so that T = 2pi(sqrt(m/k)).

The answer, however, says that I should have got T = 2pi(sqrt(k/m)), which I just don't understand... can anyone see where I've gone wrong here, or are the answers wrong?
The answer is wrong, your result is correct. If their answer was correct, would have the dimension of time. However, , , so that (inverse of time). That means that your answer is correct, as it has the dimension of time.
4. Ah, cool, thanks a lot! Glad to have been right :P

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