The figure shows a graph between velocity and displacement (from mean position) of a particle performing $SHM\,:$
Advanced
Download our app for free and get started
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} $
Download our appand 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.*
Similar Questions
- 1View SolutionTwo oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then-
- 2The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ isView Solution
- 3The amplitude of a wave represented by displacement equationView Solution
$y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be
- 4A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$View Solution
- 5On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) isView Solution
- 6A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation isView Solution
- 7A simple pendulum of length $l$ is made to oscillate with an amplitude of $45$ degrees. The acceleration due to gravity is $g$. Let $T_0=2 \pi \sqrt{l / g}$. The time period of oscillation of this pendulum will beView Solution
- 8The particle executing simple harmonic motion has a kinetic energy $K_0cos^2 \omega t$. The maximum values of the potential energy and the total energy are respectivelyView Solution
- 9A mass m is suspended from a spring of length l and force constant $K$. The frequency of vibration of the mass is ${f_1}$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is ${f_2}$. Which of the following relations between the frequencies is correctView Solution
- 10Find the ratio of time periods of two identical springs if they are first joined in series $\&$ then in parallel $\&$ a mass $m$ is suspended from them :View Solution