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May 4th, 2014, 02:31 PM   #1
Joined: May 2014
From: Lancashire England

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Unhappy Analytical Methods - Logartithms / Obtaining Expressions

Hello all!

I am new here, and in the UK doing a course on engineering. I have been really struggling with 1 assignment, which i require in for tuesday. A picture of the questions is here (may be 90 degree angle, uploaded funny):

For a) and b) on here I have worked out A) 15.34, and B) 47.925.

Apart from the 2 I answered above, I am totally confused by these
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May 4th, 2014, 06:07 PM   #2
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c) We just take logarithms of both sides, so $\log{y} = \log{kn^w} = \log{k} + w\log{n}$

The rest of that page should be straightforward.

Task 4
a) $R\sin{(wt + a)} = R\left(\sin{wt}\cos{a} + \cos{wt}\sin{a}\right)$. Comparing coefficients of $\sin{wt}$ gives you one equation, the coefficients of $\cos{wt}$ give you a second. You can then solve these simultaneous equations for $R$ and $a$.

b) Period $T = \frac{1}{f}$ and angular velocity $w = \frac{2\pi}{T}$ (you can work these equations out simply by comparing the units).

d) The equation will give an infinite number of solutions because the current is periodic. They want the one where $0 \le t \le 10 \text{ms}$.

Task 5
a) Plug the values in and see what comes out.
b) Acceleration is rate of change of velocity, or how velocity changes with respect to time. Therefore we differentiate the velocity with respect to time. Then, Newton's Second Law $F = ma$ applies. Is the force in the same direction as the velocity, or against it?
c) Put $a = 0$ and solve for $t$.
d) Velocity is the rate of change of position. So we must integrate (with respect to time) the expression for velocity to obtain an expression for the distance travelled.
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