Question

The equation of a simple harmonic motion is given as d^2x/dt^2 + ω^2x =0. where the symbols have their usual meaning. The dimension of the quantity ω^2 is
a. L^−1
b. M
c. T^−2
d. LT^−2

Answer 1

Answer on Question #83227 – Math – Differential Equations

Question

The equation of a simple harmonic motion is given as $d^2x/dt^2 + w^2x = 0$. where the symbols have their usual meaning. The dimension of the quantity $w^2$ is

a. $L^2 - 1$

b. M

c. $T^2 - 2$

d. $LT^2 - 2$

Solution

$\omega$ is the angular frequency.

$\omega$ measured in radians per second.

The dimension of the quantity $\omega$ is $T^{-1}$

So the dimension of the quantity $\omega^2$ is $T^{-2}$

Answer:

c. $T^2 - 2$

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