A particle is performing simple harmonic moti | 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 simple harmonic motion is given by $x = A \sin(\omega t)$.Given amplitude $A = 4\, cm$ and time period $T

Vedclass · Accepted Answer

$0.4$

Vedclass · Answer

(B) The equation of motion for a particle in simple harmonic motion is given by $x = A \sin(\omega t)$.Given amplitude $A = 4\, cm$ and time period $T = 1.2\, s$.To find the time taken to move from $x = 2\, cm$ to $x = 4\, cm$:At $x = 2\, cm$,$2 = 4 \sin(\omega t_1) \implies \sin(\omega t_1) = 1/2 \implies \omega t_1 = \pi/6$.At $x = 4\, cm$,$4 = 4 \sin(\omega t_2) \implies \sin(\omega t_2) = 1 \implies \omega t_2 = \pi/2$.The time taken to go from $x = 2\, cm$ to $x = 4\, cm$ is $\Delta t = t_2 - t_1 = (\pi/2 - \pi/6) / \omega = (\pi/3) / (2\pi/T) = T/6$.Since the particle returns from $x = 4\, cm$ to $x = 2\, cm$,the time taken for the return journey is also $T/6$.Total minimum time $= T/6 + T/6 = T/3$.Given $T = 1.2\, s$,total time $= 1.2 / 3 = 0.4\, s$.

Column-$I$ (Common Name)	Column-$II$ (Taxonomic category- Family)
$A$. Man	$I$. Poaceae
$B$. Datura	$II$. Anacardiaceae
$C$. Mango	$III$. Solanaceae
$D$. Wheat	$IV$. Hominidae

$A$ particle is performing simple harmonic motion along the $x$-axis with an amplitude of $4\, cm$ and a time period of $1.2\, s$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x = +4\, cm$ and back again is given by .... $s$.

Similar Questions

Which part of the ovary in mammals acts as an endocrine gland after ovulation?

If one of the roots of $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ is $-10$,then the other roots are

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

Which of the following characters are related with Poaceae family?
$(a)$ Basal placentation
$(b)$ Feathery stigma
$(c)$ Cypsela fruit
$(d)$ Pentamerous flower

Vedclass Test Series

Exam Paper Generator

Online Exam Module