MAHE Manipal B.Sc Nursing 2025
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Simple pendulum is considered one the most difficult concept.
38 Questions around this concept.
A child swinging on a swing in sitting position stands up, then the time period of the swing will :
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
What should come in place of question mark (?) in the following questions?
20% of 480 + 80% of 220 + 120 – (18)2 = ?
An ideal simple pendulum consists of a heavy point mass body suspended by a weightless, inextensible
and perfectly flexible string from rigid support about which it is free to oscillate.
When the bob is displaced to position B, through a small angle from the vertical as shown in the below figure.
Then Bob will perform SHM and its time period is given as
where
I = length of the pendulum
- key points
1. The time period of a simple pendulum is independent of the mass of the bob.
I.e If the solid bob is replaced by a hollow sphere of the same radius but different mass, the time period remains unchanged.
2.
where I is the distance between the point of suspension and the center of mass of the bob and is called effective length.
3. The period of a simple pendulum is independent of amplitude as long as its motion is simple harmonic.
Pendulum in a lift
1. The time period of a simple pendulum, If the lift is at rest or moving downward /upward with constant velocity.
where
2. The time period of a simple pendulum, If the lift is moving upward with constant acceleration a
where
3. The time period of a simple pendulum If the lift is moving downward with constant acceleration a
where
4. The time period of a simple pendulum, If the lift is moving downward with acceleration
It means there will be no oscillation in a pendulum as here
Similarly in the case of a satellite and at the center of the earth the
5. The time period of a simple pendulum whose point of suspension moving horizontally with acceleration 'a'
For the above figure
Where
6. The time period of simple pendulum accelerating down an incline
In this case
where
1.The time period of the pendulum in a liquid
If we immerse a simple pendulum in a liquid, the bob of the pendulum will experience a buoyant force in an upward direction in
addition to the other forces such as gravity and tension.
If bob a simple pendulum of density
Then the buoyant force is given as
As buoyant force will oppose its weight therefore
For the above figure let bob be displaced for a small displacement
For small displacement
and acceleration
On comparing with a standard equation of SHM,
and
and
2. The time period of the Second's pendulum
Second's Pendulum: It is that simple pendulum whose time period of vibrations is two seconds.
Putting
If the length of the pendulum is comparable to the radius of the earth
where
- Various cases
A. If
B. If
C. If
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