Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is
Diffcult
Download our app for free and get started
Net vertical force
$=\mathrm{kx}+\frac{\mathrm{kx}}{\sqrt{2}} \cos 45 \times 2=2 \mathrm{kx}=\mathrm{ma}$
$\mathrm{a}=\frac{2 \mathrm{k}}{\mathrm{m}} \mathrm{x}$
$\Rightarrow \omega=\sqrt{\frac{2 \mathrm{k}}{\mathrm{m}}}$
$\tau=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$
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
- 1As a body performs $S.H.M.$, its potential energy $U.$ varies with time as indicated inView Solution
- 2A pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ $ms ^{-1}$. (if $g=10\,m / s ^{2}$ )View Solution
- 3Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figuresView Solution
$x\left( t \right) = A\,\sin \,\left( {at + \delta } \right)$
$y\left( t \right) = B\,\sin \,\left( {bt} \right)$
Identify the correct match below
- 4The amplitude and the periodic time of a $S.H.M.$ are $ 5\,cm$ and $6\,sec$ respectively. At a distance of $2.5\,cm$ away from the mean position, the phase will beView Solution
- 5If the displacement of a particle executing $SHM $ is given by $y = 0.30\sin (220t + 0.64)$ in metre, then the frequency and maximum velocity of the particle isView Solution
- 6A body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|d x|$ is highest atView Solution
- 7The 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
- 8Two simple harmonic motions are represented by the equationsView Solution
${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$
The amplitude of second motion is ....... times the amplitude in first motion.
- 9On 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
- 10A body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\, mm$ displacement, when the amplitude of motion is $60\, mm$, is ...... $mm/s$View Solution