The figure shows a graph between velocity and displacement (from mean position) of a particle performing SHM,:

Q: The figure shows a graph between velocity and displacement (from mean position) of a particle performing $SHM\,:$

d by graph we can see that $V_{\max }=10 \mathrm{cm} / \mathrm{s}$ and $A=2.5 \mathrm{cm}$ and we know that $V_{\max }=A \omega$ $\Rightarrow 10=2.5 \omega$ $\Rightarrow \omega=4 s^{-1}$ $T=\frac{2 \pi}{4}=\frac{2 \pi}{4}=\frac{3.14}{2}=1.57 s $ $a_{\max }=A \omega^{2}=2.5 \times 4^{2}=40 \mathrm{cms}^{-2}$ $v(x=1 \mathrm{cm})=w \sqrt{A^{2}-x^{2}}=4 \sqrt{2.5^{2}-1^{2}}=4 \sqrt{5.25}=4 \sqrt{\frac{525}{100}}=4 \sqrt{\frac{21 \times 25}{100}}=$ $2 \sqrt{21} \mathrm{cm} / \mathrm{s} $

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

The figure shows a graph between velocity and displacement (from mean position) of a particle performing $SHM\,:$

Athe time period of the particle is $1.57\,s$
Bthe maximum acceleration will be $40\,cm/s^2$
Cthe velocity of particle is $2\sqrt {21} \,cm/s$ when it is at a distance $1\, cm$ from the mean position.
D
all of the above

Advanced

STD 11 Science
NEET
STD 11 - 13. oscillations
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?

($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged

($B$) The final time period of oscillation in both the cases is same

($C$) The total energy decreases in both the cases

($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases
View Solution
2
A particle starts with $S.H.M.$ from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At one time, its speed is half that of the maximum speed. What is this displacement?
View Solution
3
If displacement $x$ and velocity $v$ are related as $4v^2 = 16\, -\, x^2$ in a $SHM$ . Then time period of given $SHM$ is (consider $SI\,units$ )
View Solution
4
A rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.
View Solution
5
A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
View Solution
6
The $S.H.M.$ of a particle is given by the equations $=2 \sin \omega t+4 \cos \omega t$. Its amplitude of oscillation is ........ units
View Solution
7
A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be
View Solution
8
When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be
View Solution
9
The variation of the acceleration $a$ of the particle executing $S.H.M.$ with displacement $x$ is as shown in the figure
View Solution
10
If a simple harmonic oscillator has got a displacement of $0.02\, m$ and acceleration equal to $2.0\,m{s^{ - 2}}$ at any time, the angular frequency of the oscillator is equal to .... $rad\,{s^{ - 1}}$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free