(A) The standard equation for Simple Harmonic Motion $(SHM)$ is given by $\frac{d^2x}{dt^2} + \omega^2x = 0$.Comparing the given equation $\frac{d^2x}

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) The standard equation for Simple Harmonic Motion $(SHM)$ is given by $\frac{d^2x}{dt^2} + \omega^2x = 0$.Comparing the given equation $\frac{d^2x}{dt^2} + \pi^2x = 0$ with the standard equation,we get $\omega^2 = \pi^2$.Taking the square root,we find $\omega = \pi \, rad/s$.The relationship between angular frequency $\omega$ and frequency $f$ is given by $\omega = 2\pi f$.Therefore,$f = \frac{\omega}{2\pi} = \frac{\pi}{2\pi} = 0.5 \, Hz$.

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

Medium

The equation of motion of a particle of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

A
$0.5$
B
$2$
C
$5\sqrt{10}$
D
$\frac{1}{5\sqrt{10}}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Oscillations

Subtopic

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

$A$ simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation: $y = 5 \sin \pi (t + 4) \ m$. Then the values of $A$ (in $m$) and $T$ (in $sec$) are:

Medium

View Solution

Show that simple harmonic motion may be regarded as the projection of uniform circular motion along a diameter of the circle.

Medium

View Solution

What is constant in $S.H.M.$?

Easy

View Solution

Which of the following functions of time represent $(a)$ simple harmonic motion and $(b)$ periodic but not simple harmonic? Give the period for each case.
$(1)$ $\sin \omega t - \cos \omega t$
$(2)$ $\sin^2 \omega t$

Medium

View Solution

Can an oscillatory motion be non-periodic?

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The equation of motion of a particle of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

Similar Questions

$A$ simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation: $y = 5 \sin \pi (t + 4) \ m$. Then the values of $A$ (in $m$) and $T$ (in $sec$) are:

Show that simple harmonic motion may be regarded as the projection of uniform circular motion along a diameter of the circle.

What is constant in $S.H.M.$?

Which of the following functions of time represent $(a)$ simple harmonic motion and $(b)$ periodic but not simple harmonic? Give the period for each case.$(1)$ $\sin \omega t - \cos \omega t$$(2)$ $\sin^2 \omega t$

Can an oscillatory motion be non-periodic?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Which of the following functions of time represent $(a)$ simple harmonic motion and $(b)$ periodic but not simple harmonic? Give the period for each case.
$(1)$ $\sin \omega t - \cos \omega t$
$(2)$ $\sin^2 \omega t$