A particle starts from a point P at a distanc | vedclass

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

Question

(D) The general equation for $SHM$ is $x = A \cos(\omega t + \phi)$.At $t = 0$,the particle is at $x = A/2$ and moving towards the left (towards the m

Vedclass · Accepted Answer

$x = A \cos \left( \frac{2\pi}{T}t + \frac{\pi}{3} \right)$

Vedclass · Answer

(D) The general equation for $SHM$ is $x = A \cos(\omega t + \phi)$.At $t = 0$,the particle is at $x = A/2$ and moving towards the left (towards the mean position $O$).Substituting $t = 0$ and $x = A/2$ into the equation: $A/2 = A \cos(\phi)$,which gives $\cos(\phi) = 1/2$.This implies $\phi = \pm 60^{\circ}$ or $\pm \pi/3$ radians.Since the particle is moving towards the left (towards the negative direction) from a positive displacement,the velocity $v = dx/dt = -A\omega \sin(\omega t + \phi)$ must be negative at $t = 0$.Thus,$-A\omega \sin(\phi)  0$.Therefore,$\phi = +60^{\circ} = \pi/3$.Substituting $\omega = 2\pi/T$ and $\phi = \pi/3$,the equation of motion is $x = A \cos \left( \frac{2\pi}{T}t + \frac{\pi}{3} \right)$.

$A$ particle starts from a point $P$ at a distance of $A/2$ from the mean position $O$ and travels towards the left as shown in the figure. If the time period of $SHM$ executed about $O$ is $T$ and the amplitude is $A$,then the equation of motion of the particle is:

Similar Questions

$A$ sonometer wire has a length of $114 ~cm$ between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in $cm$) whose fundamental frequencies are in the ratio $1:3:4$?

How many cyclic structures are possible for $C_4H_6$?

Two infinite length wires carry currents $8A$ and $6A$ respectively and are placed along the $X$ and $Y$-axes. The magnetic field at a point $P(0, 0, d) \ m$ will be:

$A$ big liquid drop splits into $n$ similar small drops under isothermal conditions. Then, in this process:

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module