CBSE Class 11-science - More Examples of Bodies in SHM Videos
Oscillations
This video explains categorising the oscillations of a wooden floating cylinder and oscillations of a liquid in a U-shaped tube as simple harmonic motions.
- What will be the period of oscillation of a simple pendulum of length 100 cm in a spaceship in a geostationary orbit?
- Write the formula for the time period of a liquid column of length L, oscillating in a U-tube.
- A vertical U-tube of uniform cross-section contains water up to a height of 20 cm. Calculate the time-period of the oscillation of water when it is disturbed.
- A cylindrical wooden block of cross-section 15 cm^{2} and mass 230 g is floated over water with an extra weight of 50 g attached to its bottom. The cylinder floats vertically. From the state of equilibrium, it is slightly depressed, and released. Deduce the frequency of oscillation of the block.
- A horizontal platform with an object placed on it is excuting SHM in the vertical direction. The amplitude of oscillation is 2.5 cm. What must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10 ms^{-2}.
- A sphere is hung at the end of a wire, and 30^{o} rotation of the sphere about the wire generates a restoring torque of 4.6 Nm. If the moment of inertia of the sphere is 0.082 kg m^{2}, deduce the frequency of angular oscillations.
- Derive an expression for the time-period and frequency of oscillation of a cylindrical wooden block floating over water when it is slightly depressed, and released from the state of equilibrium.
- Show that for a liquid contained in a U-tube and vibrating simple harmonically, the frequency
- If the earth were a homogeneous sphere and a straight hole bored in it through its centre, show that if a body were dropped into the hole it would execute a simple harmonic motion. Also find its time period.
- Show that motion of cylinder floating in the liquid is simple harmonic motion and find the time period of oscillations.