Question

If s is distance and t is time, what must be the dimensions of a and b in the equation
s=asin(bt)
?


[a]=[L]−1
,
[b]=[L]−1

[a]=[T]−1
,
[b]=[L]

[a]=[L]
,
[b]=[T]−1

[a]=[L]2
,
[b]=[T]−2

Answer 1

Answer on Question#52046 - Physics - Mechanics

If $s$ is distance and $t$ is time, what must be the dimensions of $a$ and $b$ in the equation $s = a \sin(bt)$?

$$\begin{array}{l} [a] = [L] - 1, [b] = [L] - 1 \\ [a] = [T] - 1, [b] = [L] \\ [a] = [L], [b] = [T] - 1 \\ [a] = [L] \cdot 2, [b] = [T] - 2 \\ \end{array}$$

**Solution:**

The argument of sine should be dimensionless, so the dimensions of $b$ should be $T^{-1}$. Since dimensions of $s$ are $L$, the dimensions of $b$ are also $L$.

**Answer:** $[a] = [L], [b] = [T]^{-1}$.

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