Define periodic time and frequency. State their $SI$ units,dimensional formulas,and the relationship between them.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Periodic Time: The smallest interval of time after which the motion is repeated is called its period. It is the time required to complete one oscillation. It is denoted by $T$. Its $SI$ unit is second $(s)$. The dimensional formula is $[M^0 L^0 T^1]$.
Frequency: The number of oscillations completed in one second is called frequency. It is denoted by $f$ or $\nu$. Its $SI$ unit is $Hz$ (Hertz) or $s^{-1}$. The dimensional formula is $[M^0 L^0 T^{-1}]$.
Relationship: Frequency is the reciprocal of periodic time. Mathematically,$f = \frac{1}{T}$ or $T = \frac{1}{f}$.

Explore More

Similar Questions

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

The displacement of a particle from its mean position (in metre) is given by
$y = 0.2 \sin (10 \pi t + 1.5 \pi) \cos (10 \pi t + 1.5 \pi)$
The motion of the particle is

What is the importance of periodic $\text{sine}$ and $\text{cosine}$ functions in physics?

The motion of a particle varies with time according to the relation $y = a(\sin \omega \,t + \cos \omega \,t)$,then

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.
$(1)$ $\sin \omega t - \cos \omega t$
$(2)$ $\sin^2 \omega t$

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