First slide

Simple harmonic motion

Question

The equation of motion of a particle executing simple harmonic motion is given by $a + 36 π^{2} x = 0$ , where a is acceleration and x is displacement. Then, its frequency of oscillation is (in hertz)

Moderate

A

3
B

6
C

9
D

4

Solution

A simple harmonic motion can be represented by the equation $a = - ω^{2} x$ .
Comparing the given equation $a + 36 π^{2} x = 0$ in the above form, we get $ω^{2} = 36 π^{2}$ .
Taking square root on both sides $ω = 6 π$
Using the relation $ω = 2 π f$ , $6 π = 2 π f$
The frequency of oscillation $f = 3 H z$

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