A particle executes a simple harmonic motion | vedclass

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

Question

(C) The displacement of a particle in simple harmonic motion starting from the mean position is given by $x(t) = A \sin(\omega t)$, where $A$ is the a

Vedclass · Accepted Answer

$\sqrt{2} - 1$

Vedclass · Answer

(C) The displacement of a particle in simple harmonic motion starting from the mean position is given by $x(t) = A \sin(\omega t)$, where $A$ is the amplitude and $\omega = \frac{2\pi}{T} = \frac{2\pi}{8} = \frac{\pi}{4} 	ext{ rad/s}$.At $t = 0$, $x(0) = 0$.At $t = 1 	ext{ s}$, $x(1) = A \sin(\frac{\pi}{4} 	imes 1) = A \sin(45^\circ) = \frac{A}{\sqrt{2}}$.Distance traveled in the $1^{st}$ second is $d_1 = |x(1) - x(0)| = \frac{A}{\sqrt{2}}$.At $t = 2 	ext{ s}$, $x(2) = A \sin(\frac{\pi}{4} 	imes 2) = A \sin(90^\circ) = A$.Distance traveled in the $2^{nd}$ second is $d_2 = |x(2) - x(1)| = |A - \frac{A}{\sqrt{2}}| = A(1 - \frac{1}{\sqrt{2}}) = A(\frac{\sqrt{2} - 1}{\sqrt{2}})$.The ratio of distance traveled in the $2^{nd}$ second to the $1^{st}$ second is $\frac{d_2}{d_1} = \frac{A(\frac{\sqrt{2} - 1}{\sqrt{2}})}{\frac{A}{\sqrt{2}}} = \sqrt{2} - 1$.

Similar Questions

The period of $S.H.M.$ of a particle is $16 \ s$. The phase difference between the positions at $t = 2 \ s$ and $t = 4 \ s$ will be

$A$ particle is executing simple harmonic motion. Its amplitude is $A$ and time period is $5 \text{ sec}$. The time required by it to move from $x = A$ to $x = A/\sqrt{2}$ is . . . . . . sec.

The periodic time of a particle doing simple harmonic motion is $4 \,s$. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

$A$ particle is executing $SHM$. The time taken for $\left(\frac{3}{8}\right)^{\text{th}}$ of an oscillation from extreme positions is $x$. Then,the time taken for the particle to complete $\left(\frac{5}{8}\right)^{\text{th}}$ of an oscillation from the mean position is

Vedclass Test Series

Exam Paper Generator

Online Exam Module