Differential equation for a particle performing linear SHM is given by `(d^(2)x)/(dt^(2))+3xx=0`, where x is the displacement of the particle. The frequency of oscillatory motion is

Options

A. `(1)/(pisqrt(2))` per sec
B. `(sqrt(3))/(2pi)` per sec
C. `sqrt((3)/(pi))`
D. `(asqrt(2))/(pi)` per sec

Explanation

To find the frequency of oscillatory motion for a particle performing linear simple harmonic motion (SHM) given the differential equation:

\[ \frac{d^2x}{dt^2} + 3x = 0 \]

we can follow these steps:

### Step 1: Identify the standard form of SHM
The standard form of the differential equation for simple harmonic motion is:

\[ \frac{d^2x}{dt^2} + \omega^2 x = 0 \]

where \(\omega\) is the angular frequency.

### Step 2: Compare the given equation with the standard form
From the given equation:

\[ \frac{d^2x}{dt^2} + 3x = 0 \]

we can see that it matches the standard form where \(\omega^2 = 3\).

### Step 3: Solve for \(\omega\)
To find \(\omega\), we take the square root of both sides:

\[ \omega = \sqrt{3} \]

### Step 4: Calculate the frequency
The frequency \(f\) is related to the angular frequency \(\omega\) by the formula:

\[ f = \frac{\omega}{2\pi} \]

Substituting the value of \(\omega\):

\[ f = \frac{\sqrt{3}}{2\pi} \]

### Step 5: Final answer
Thus, the frequency of the oscillatory motion is:

\[ f = \frac{\sqrt{3}}{2\pi} \, \text{Hz} \]