The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is
Medium
Download our app for free and get started
(b)Total potential energy $= 0.04 J$
Resting potential energy $=0.01 J$
Maximum kinetic energy $=(0.04-0.01)$
$ = 0.03J = \frac{1}{2}m\;{\omega ^2}{a^2} = \frac{1}{2}k{a^2}$
$0.03 = \frac{1}{2} \times k \times {\left( {\frac{{20}}{{1000}}} \right)^2}$
$k = 0.06 \times 2500\;N/m = 150\;N/m$.
Resting potential energy $=0.01 J$
Maximum kinetic energy $=(0.04-0.01)$
$ = 0.03J = \frac{1}{2}m\;{\omega ^2}{a^2} = \frac{1}{2}k{a^2}$
$0.03 = \frac{1}{2} \times k \times {\left( {\frac{{20}}{{1000}}} \right)^2}$
$k = 0.06 \times 2500\;N/m = 150\;N/m$.
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
- 1A pendulum has time period $T$. If it is taken on to another planet having acceleration due to gravity half and mass $ 9 $ times that of the earth then its time period on the other planet will beView Solution
- 2A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant isView Solution
- 3A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given byView Solution
- 4The motion of a particle varies with time according to the relation $y = a(\sin \omega \,t + \cos \omega \,t)$, thenView Solution
- 5A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is nowView Solution
- 6When a mass $M$ is attached to the spring of force constant $k$, then the spring stretches by $l$. If the mass oscillates with amplitude $l$, what will be maximum potential energy stored in the springView Solution
- 7A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.View Solution
- 8A simple pendulum is attached to a block which slides without friction down an inclined plane $A B C$ having an angle of inclination $\alpha$ as shown below. While the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string isView Solution
- 9A simple harmonic motion is represented by $F(t) = 10\sin \,(20\,t + 0.5)$. The amplitude of the $S.H.M.$ is $a$ $=$ ....View Solution
- 10A solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid $\rho(> \rho_0)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will beView Solution
