The function (sin omega t - cos omega t) repr | vedclass

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

Question

(B) Given function: $x = \sin \omega t - \cos \omega t$We can rewrite this as: $x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{

Vedclass · Accepted Answer

a simple harmonic motion with a period $\frac{2\pi}{\omega}$

Vedclass · Answer

(B) Given function: $x = \sin \omega t - \cos \omega t$We can rewrite this as: $x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t \right)$Using the trigonometric identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$,where $B = \frac{\pi}{4}$:$x = \sqrt{2} \sin \left( \omega t - \frac{\pi}{4} \right)$Comparing this with the standard equation of Simple Harmonic Motion $(SHM)$: $x = A \sin(\omega t + \phi)$:Here,amplitude $A = \sqrt{2}$ and angular frequency is $\omega$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Since the function can be expressed in the form $A \sin(\omega t + \phi)$,it represents a simple harmonic motion with a period of $\frac{2\pi}{\omega}$.

The function $(\sin \omega t - \cos \omega t)$ represents

Similar Questions

The displacement of a particle executing $S.H.M.$ is given by $x = 0.01 \sin 100 \pi(t + 0.05)$. The time period is ........ $s$.

$A$ point particle of mass $0.1 \ kg$ is executing $S.H.M.$ with an amplitude of $0.1 \ m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \ J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^{\circ}$.

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

The equation of $SHM$ of a particle is given as $2 \frac{d^2x}{dt^2} + 32x = 0$,where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module