Given below are two statements. One is labell | vedclass

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

Question

(D) For a simple harmonic motion,the position is given by $x(t) = A \sin(\omega t + \phi)$.At $t = 0$,$x_0 = A \sin \phi$  $..........(1)$The momentum

Vedclass · Accepted Answer

Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.

Vedclass · Answer

(D) For a simple harmonic motion,the position is given by $x(t) = A \sin(\omega t + \phi)$.At $t = 0$,$x_0 = A \sin \phi$  $..........(1)$The momentum is $p(t) = m \frac{dx}{dt} = m A \omega \cos(\omega t + \phi)$.At $t = 0$,$p_0 = m A \omega \cos \phi$  $..........(2)$From equations $(1)$ and $(2)$,we can solve for the two unknowns,amplitude $A$ and phase constant $\phi$,using the initial conditions $x_0$ and $p_0$.Specifically,$	an \phi = \frac{m \omega x_0}{p_0}$ and $A = \sqrt{x_0^2 + (p_0 / m \omega)^2}$.Since $A$ and $\phi$ are uniquely determined by $x_0$ and $p_0$,the state of the system at any time $t$ is fully determined.Thus,both Assertion $(A)$ and Reason $(R)$ are true,and $(R)$ is the correct explanation of $(A)$.

Similar Questions

The equation of motion of a particle is given by $x = a \sin(50t + \frac{\pi}{3}) \text{ cm}$. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are . . . . . . .

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.

The displacement of a particle varies according to the relation $x = 3 \sin 100t + 8 \cos^2 50t$. Which of the following is/are correct about this motion?

$A$ particle is executing simple harmonic motion with an instantaneous displacement $x = A \sin^2(\omega t - \frac{\pi}{4})$. The time period of oscillation of the particle is

$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module