(C) The given equation is $4 \frac{d^{2} y}{d t^{2}}+9 y=0$.Rearranging the equation,we get $\frac{d^{2} y}{d t^{2}} = -\frac{9}{4} y$.Comparing this

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(C) The given equation is $4 \frac{d^{2} y}{d t^{2}}+9 y=0$.Rearranging the equation,we get $\frac{d^{2} y}{d t^{2}} = -\frac{9}{4} y$.Comparing this with the standard Simple Harmonic Motion $(SHM)$ equation $\frac{d^{2} y}{dt^{2}} = -\omega^{2} y$,where $\omega$ is the angular frequency:$\omega^{2} = \frac{9}{4}$.Taking the square root of both sides,we get $\omega = \sqrt{\frac{9}{4}} = \frac{3}{2} = 1.5 \text{ rad/s}$.

Class 11 Physics Oscillations Periodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM

Medium

The angular frequency of motion whose equation is $4\frac{d^2y}{dt^2} + 9y = 0$ is ($y =$ displacement and $t =$ time).

A
$2.25$
B
$0.44$
C
$1.5$
D
$0.67$

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Chapter

Oscillations

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Periodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM

The function $x = A \sin^2 \omega t + B \cos^2 \omega t + C \sin \omega t \cos \omega t$ does not represent $SHM$ for which of the following conditions?

Difficult

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If the function $\sin^2 \omega t$ (where $t$ is time in seconds) represents a periodic motion,then the period of the motion is:

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For a simple harmonic motion represented by the equation $y = 0.30 \sin (220 \, t + 0.64) \ m$,what are the frequency and maximum velocity,respectively?

Medium

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If the displacement of a particle is given by $x = 3 \sin (5\pi t) + 4 \cos (5\pi t) \text{ cm}$,what is the amplitude of the particle?

Medium

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Draw plots for initial phase $\phi = 0$ for different periods.

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The angular frequency of motion whose equation is $4\frac{d^2y}{dt^2} + 9y = 0$ is ($y =$ displacement and $t =$ time).

Similar Questions

The function $x = A \sin^2 \omega t + B \cos^2 \omega t + C \sin \omega t \cos \omega t$ does not represent $SHM$ for which of the following conditions?

If the function $\sin^2 \omega t$ (where $t$ is time in seconds) represents a periodic motion,then the period of the motion is:

For a simple harmonic motion represented by the equation $y = 0.30 \sin (220 \, t + 0.64) \ m$,what are the frequency and maximum velocity,respectively?

If the displacement of a particle is given by $x = 3 \sin (5\pi t) + 4 \cos (5\pi t) \text{ cm}$,what is the amplitude of the particle?

Draw plots for initial phase $\phi = 0$ for different periods.

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