In the situation as shown in figure time period of vertical oscillation of block for small displacements will be
Advanced
Download our app for free and get started
Let block be displaced through $x$ in downward
direction and elongation in spring $=\mathrm{x}_{1}$ then
$x \cos \theta=x_{1}$ $...(1)$
Restoring force $\mathrm{F}=2 \mathrm{kx}_{1} \cos \theta$
$\mathrm{F}=2 \mathrm{k} \cos ^{2} \theta \times$
Hence $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \cos ^{2} \theta}}=2 \pi \sec \theta \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$
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
- 1A 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
- 2View SolutionThe value of maximum possible amplitude in the case of forced oscillations when driving frequency is close to natural frequency is
- 3The displacement of a particle from its mean position (in metre) is given byView Solution
$y = 0.2\sin \left( {10\pi t + 1.5\pi } \right)\cos \left( {10\pi t + 1.5\pi } \right)$
The motion of particle is
- 4The motion of a particle as per $x=Asin \omega t + Bcos\omega t$ is :-View Solution
- 5A 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
- 6A uniform disc of mass $M$ and radius $R$ is suspended in vertical plane from a point on its periphery. Its time period of oscillation is ........View Solution
- 7The displacement of a particle varies according to the relation $x = 3 \ sin\ 100t + 8\ cos^2\ 50t$ . Which of the following is incorrect about this motionView Solution
- 8The mass of a particle is $1\,\,kg$ and it is moving along $x-$ axis. The period of its small oscillation is $\frac {\pi }{2}$ . Its potential energy may beView Solution
- 9View SolutionIn a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic?
- 10The phase of a particle executing simple harmonic motion is $\frac{\pi }{2}$ when it hasView Solution