The displacement of a body executing SHM is g | vedclass

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

Question

(A) The displacement equation is $x = A \sin (2\pi t + \pi /3).$Velocity $v$ is given by the derivative of displacement with respect to time: $v = \fr

Vedclass · Accepted Answer

$0.33$

Vedclass · Answer

(A) The displacement equation is $x = A \sin (2\pi t + \pi /3).$Velocity $v$ is given by the derivative of displacement with respect to time: $v = \frac{dx}{dt} = A(2\pi) \cos (2\pi t + \pi /3).$Velocity is maximum when the magnitude of the cosine term is maximum,which occurs at the mean position where $x = 0$.Setting $x = 0$,we get $\sin (2\pi t + \pi /3) = 0$.This implies the argument $(2\pi t + \pi /3) = n\pi$,where $n$ is an integer.For $n = 0$,$2\pi t = -\pi /3$,which gives $t For $n = 1$,$2\pi t + \pi /3 = \pi$.$2\pi t = \pi - \pi /3 = 2\pi /3$.$t = 1/3 \approx 0.33 	ext{ s}$.Thus,the first time after $t = 0$ when the velocity is maximum is $0.33 	ext{ s}$.

The displacement of a body executing $SHM$ is given by $x = A \sin (2\pi t + \pi /3).$ The first time from $t = 0$ when the velocity is maximum is .... $\sec$

Similar Questions

$A$ body executing $S.H.M.$ along a straight line has a velocity of $3 \, m/s$ when it is at a distance of $4 \, m$ from its mean position and $4 \, m/s$ when it is at a distance of $3 \, m$ from its mean position. Its angular frequency and amplitude are:

The maximum velocity of a particle performing simple harmonic motion is $6.28 \text{ cm s}^{-1}$. If the length of its path is $8 \text{ cm}$, then what is its period (in $\text{ s}$)?

The velocity of a particle executing $S.H.M.$ varies with displacement $(x)$ as $4V^2 = 50 - x^2$. The time period of oscillation is $\frac{x}{7}$ seconds. The value of '$x$' is (Take $\pi = \frac{22}{7}$)

$A$ particle is executing $S.H.M.$ If its amplitude is $2 \, m$ and periodic time is $2 \, s$,then the maximum velocity of the particle will be:

What is the phase difference between the velocity and displacement of a particle executing $SHM$ (in $^{\circ}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module