A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$
Advanced
Download our app for free and get started
$\mathrm{b}=\frac{\mathrm{F}}{\mathrm{v}}=\frac{120}{1}, \mathrm{r}=\frac{\mathrm{b}}{2 \mathrm{m}}=\frac{60}{7000 \times 2}$
$\omega=\sqrt{\omega_{0}^{2}-r^{2}}$
$\mathrm{kx}=\mathrm{F}$
$\mathrm{k}=\frac{450}{2}=225=\sqrt{\frac{225}{700}-\frac{60^{2}}{700^{2}}}$
$=\sqrt{\frac{225 \times 700-3600}{700^{2}}}=0.56 \mathrm{rad} / \mathrm{s}$
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
- 1A loaded vertical spring executes $S.H.M.$ with a time period of $4\; sec$. The difference between the kinetic energy and potential energy of this system varies with a period of ........$sec$View Solution
- 2In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip atView Solution
- 3A mass on a vertical spring begins its motion at rest at $y = 0\ cm$. It reaches a maximum height of $y = 10\ cm$. The two forces acting on the mass are gravity and the spring force. The graph of its kinetic energy ($KE$) versus position is given below. Net force on the mass varies with $y$ asView Solution
- 4A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :View Solution
- 5Equations $y = 2A \cos ^2 \omega \,t$ and $y = A (\sin \omega t + \cos \omega t )$ represent the motion of two particles.View Solution
- 6A spring mass system preforms $S.H.M.$ If the mass is doubled keeping amplitude same, then the total energy of $S.H.M.$ will become :View Solution
- 7A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will beView Solution
- 8A simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string isView Solution
- 9Two simple harmonic motions are represented by the equations ${y_1} = 0.1\sin \left( {100\pi t + \frac{\pi }{3}} \right)$ and ${y_2} = 0.1\cos \pi t.$ The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ isView Solution
- 10A block of mass $1 \,kg$ attached to a spring is made to oscillate with an initial amplitude of $12\, cm$. After $2\, minutes$ the amplitude decreases to $6\, cm$. Determine the value of the damping constant for this motion. (take In $2=0.693$ )View Solution