A particle is executing simple harmonic motio | vedclass

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

Question

(B) The general equation for displacement in $SHM$ is given by $x(t) = a \cos(\omega t + \phi)$,where $a$ is the amplitude,$\omega$ is the angular fre

Vedclass · Accepted Answer

$x = a \cos(\frac{\pi}{2}t + \frac{\pi}{4})$

Vedclass · Answer

(B) The general equation for displacement in $SHM$ is given by $x(t) = a \cos(\omega t + \phi)$,where $a$ is the amplitude,$\omega$ is the angular frequency,and $\phi$ is the initial phase angle.Given the time period $T = 4 \ s$,the angular frequency is $\omega = \frac{2\pi}{T} = \frac{2\pi}{4} = \frac{\pi}{2} \ 	ext{rad/s}$.At $t = 0$,the particle is at an angle of $45^\circ$ with the $x$-axis,so the initial phase $\phi = 45^\circ = \frac{\pi}{4} \ 	ext{rad}$.Substituting these values into the general equation,we get $x(t) = a \cos(\frac{\pi}{2}t + \frac{\pi}{4})$.Thus,the correct option is $B$.

$A$ particle is executing simple harmonic motion $(SHM)$ with a time period $T = 4 \ s$. At $t = 0$,the particle is at a position where its angular position is $45^\circ$ with the $x$-axis. Find the displacement equation of the particle along the $x$-axis.

Similar Questions

Explain the concepts of a reference particle and a reference circle,and show that simple harmonic motion $(SHM)$ is the projection of uniform circular motion on a diameter of the reference circle.

$A$ particle is performing $SHM$ according to the equation $x = (3\, cm) \sin \left( \frac{2\pi t}{18} + \frac{\pi}{6} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$.

Two equations of two $S.H.M.$ are $y = a\sin(\omega t - \alpha)$ and $y = b\cos(\omega t - \alpha)$. The phase difference between the two is .... $^\circ$.

$A$ particle executes simple harmonic motion with an amplitude '$A$'. The distance travelled by it in one periodic time is

$A$ particle executing $SHM$ of amplitude $a$ has a displacement of $-\frac{a}{2}$ at $t = \frac{T}{4}$ and a positive velocity. Find the initial phase of the particle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module