A particle performs simple harmonic motion wi | vedclass

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

Question

(B) The equation of motion for a particle in $SHM$ passing through the origin at $t=2 \ s$ is $x(t) = A \sin(\omega(t - 2))$.Given $T = 16 \ s$, the a

Vedclass · Accepted Answer

$\frac{32 \sqrt{2}}{\pi}$

Vedclass · Answer

(B) The equation of motion for a particle in $SHM$ passing through the origin at $t=2 \ s$ is $x(t) = A \sin(\omega(t - 2))$.Given $T = 16 \ s$, the angular frequency is $\omega = \frac{2 \pi}{T} = \frac{2 \pi}{16} = \frac{\pi}{8} \ rad/s$.The velocity is $v(t) = \frac{dx}{dt} = A \omega \cos(\omega(t - 2))$.At $t = 4 \ s$, $v = 4 \ m/s$:$4 = A \left(\frac{\pi}{8}ight) \cos\left(\frac{\pi}{8}(4 - 2)ight)$$4 = A \left(\frac{\pi}{8}ight) \cos\left(\frac{\pi}{4}ight)$$4 = A \left(\frac{\pi}{8}ight) \left(\frac{1}{\sqrt{2}}ight)$$A = \frac{4 	imes 8 	imes \sqrt{2}}{\pi} = \frac{32 \sqrt{2}}{\pi} \ m$.

$A$ particle performs simple harmonic motion with a time period of $16 \ s$. At a time $t=2 \ s$, the particle passes through the origin and at $t=4 \ s$ its velocity is $4 \ m/s$. The amplitude of the motion is

Similar Questions

The velocity at the mean position of a particle executing $S.H.M.$ is $v$. What is the velocity of the particle at a distance equal to half of the amplitude?

$A$ spring executes $S$.$H$.$M$. with mass $10 \text{ kg}$ attached to it. The force constant of spring is $10 \text{ N/m}$. If at any instant its velocity is $40 \text{ cm/s}$, the displacement at that instant is (Amplitude of $S$.$H$.$M$. is $0.5 \text{ m}$) (in $\text{ m}$)

$Assertion :$ For a particle performing $SHM$,its speed decreases as it goes away from the mean position.
$Reason :$ In $SHM$,the acceleration is always opposite to the velocity of the particle.

The maximum speed of a particle in $S.H.M.$ is $V$. The average speed is

The displacement of a particle executing $SHM$ is given by $y = 0.25 \sin(200t) \ cm$. The maximum speed of the particle is $......... \ cm \ s^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module