A hollow sphere is filled with water through a small hole in it. It is hung by a long thread and, as the water flows out of the hole at the bottom, one finds that the period of oscillation first increases and then decreases. Explain.

From figure it can be noted that amplitude decreases exponentially which is the case for a damped oscillation,

A undamped oscillation isn't acted by any opposing force meaning it oscillates indefinitely.

But a damped oscillation is acted by another opposing force of damping constant b which is what we see in our daily life.

where,tau is damping time constant that is the time taken to decrease exponentially by 1/e of its initial value and

Since, the mechanical engineers doesn't want unwanted and...

In the block-spring system, the inertia is concentrated in a single element of the system which is the block, but in the string the inertia is distributed throughout the system. Similarly, the elasticity of the block-spring system is lumped in one element ( spring) but in the vibrating spring it is distributed throughout the system. Although there is only one way for the block-spring system to store kinetic and potential energy, the vibrating spring has an infinite number of ways to store its...

When a singer holds a note of a particular frequency which is equal to the natural frequency of the glass, it will vibrate with great amplitudes. As a result the glass may be blown apart in pieces.

If the glass quality is low, the resonance frequency cannot be matched with its right natural frequency. That is why it cannot be done if the glassware quality is low

The time period (T) of a simple pendulum is defined as,

T = 2π L/g

Here, L is the length of the pendulum and g is the acceleration due to gravity.

So the period of oscillation is independent of mass but depends on length. Thus length and time period is the fundamental property of a pendulum. Therefore, length and time be based on properties of a pendulum but the mass does not.

Practically, it is impossible to create an ideal simple pendulum because we can’t have a point mass and heavy solid metallic sphere (bob) tied to one end of a long unspun cotton thread and suspended from rigid support to serve the purpose of a simple pendulum.

When we sit in a in a straight-backed chair, our centre of gravity is lower and we are more stable and when we try to stand up without leaning forward, we can't do this because when we apply a force on our body and a torques is produced but the line of action not going outside the base and we get back to our position that's why we can't do this

To distinguish between a hard boiled egg and a raw egg, we spin each on a table top. The egg which spins at a slower rate shall be a raw egg. This is because in a raw egg, liquid matter inside tries to get away from the axis of rotation. Therefore, its moment of inertia I increases.

As τ=Iα =constant, therefore, α decreases, i.e., raw egg will spin with smaller angular acceleration. The reverse is true for a hard boiled egg which will rotate more or less like a rigid body.

1.ans: No the tension in the string of a simple pendulum is not constant throughout the motion

v is velocity of the bob and theta is the angle made by the string with vertical axis.as v andθboth are variable T is also variable.T is maximum at mean position as at mean position v is max and the angle is minimum.

2.ans: If the amplitude of the simple harmonic oscillator is doubled then: ...

Some of the familiar periodic motions are a vibrating tuning fork, the Earth revolving around the Sun, a swing in motion, a water wave, and a working pendulum. Simple harmonic motion is a distinct instance of periodic motion. A water wave, the swing and the tuning fork perform simple harmonic motions. On the other hand, the revolution of the Earth and the bouncing ball do not follow the principles of harmonic motion.