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I saw an exercise where you had to calculate the units of $C_i, i=1,2$ from an equation like this:

  • $v^2=2\cdot C_1x$ and
  • $x=C_1\cdot \cos(C_2\cdot t)$

where

  • $x$ means meters,
  • $t$ means seconds and
  • $v$ means velocity.

For $C_1$ I got $C_1=m/s^2$. But coming to $C_2$ the cosinus irritates me somehow:

$$x=C_1 \cdot \cos(C_2 t)\Rightarrow m=m/s^2 \cdot \cos(C_2 s)\Rightarrow s^2 = \cos(C_2 s)$$

Does this mean, that $C_2$ must have the unit $s$?

Thanks a lot!

Qmechanic
  • 220,844
Aufwind
  • 205

2 Answers2

10

Trigonometric functions don't "preserve" units. The expression under a trigonometric function must be dimensionless and so is the value of a trigonometric function.

Thus, C2 in your equations is in units of frequency: Hz or 1/s.

There is an error in one of the equations, perhaps a missing constant.

Adam Zalcman
  • 4,952
0

I know where you have done the mistake . I have solved this question earlier and thus in the second case we don't need to take the dimensions of C1 as obtained in our first case . Now if you solve it as @Adam said the correct answer would be Hertz

Pooja Shukla
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