Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
MediumDraw plots for initial phase $\phi = 0$ for different periods.
(N/A) The general equation for simple harmonic motion is $x(t) = A \sin(\omega t + \phi)$.
Given the initial phase $\phi = 0$,the equation becomes $x(t) = A \sin(\omega t)$.
This represents a sine wave starting from the origin at $t = 0$. However,if the motion starts from the extreme position,the equation is $x(t) = A \cos(\omega t)$.
The provided graph shows displacement versus time for two different periods.
In this plot,curve $(b)$ has half the period $(T_b = T_a / 2)$ and twice the frequency $(f_b = 2f_a)$ compared to curve $(a)$.
Given the initial phase $\phi = 0$,the equation becomes $x(t) = A \sin(\omega t)$.
This represents a sine wave starting from the origin at $t = 0$. However,if the motion starts from the extreme position,the equation is $x(t) = A \cos(\omega t)$.
The provided graph shows displacement versus time for two different periods.
In this plot,curve $(b)$ has half the period $(T_b = T_a / 2)$ and twice the frequency $(f_b = 2f_a)$ compared to curve $(a)$.
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For particle $P$ revolving around the centre $O$ with radius of circular path $r$ and angular velocity $\omega$,as shown in the figure,the projection of $OP$ on the $x$-axis at time $t$ is .................
The amplitude and the time period in a $S.H.M.$ are $0.5\, cm$ and $0.4\, s$ respectively. If the initial phase is $\pi/2$ radian,then the equation of $S.H.M.$ will be:
Medium
View SolutionThe displacement of a particle performing $S.H.M.$ is given by $Y = A \cos [\pi(t + \phi)]$. If at $t = 0$,the displacement is $y = 2 \text{ cm}$ and velocity is $v = 2\pi \text{ cm/s}$,the value of amplitude $A$ in $\text{cm}$ is:
Two particles are executing Simple Harmonic Motion ($S$.$H$.$M$.). The equations of their motion are $y_1 = 10 \sin \left( \omega t + \frac{\pi}{4} \right)$ and $y_2 = 25 \sin \left( \omega t + \frac{\sqrt{3} \pi}{4} \right)$. What is the ratio of their amplitudes?
Easy
View Solution$A$ body oscillates with $SHM$ according to the equation (in $SI$ units):
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.
Medium
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