Oscillation Of Pendulum - Practice Questions & MCQ

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.

• The time period of oscillation of simple pendulum (T)-

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 

m=mass of the bob 

l = length of pendulum 

g = acceleration due to gravity.

• 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 l is the distance between the point of suspension and center of mass of 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 

 the length of pendulum

 acceleration due to gravity.

2.The time period of a simple pendulum, If the lift is moving upward with constant acceleration a

where 

 the length of pendulum

 acceleration due to gravity.

 acceleration of pendulum.

3. The time period of simple pendulum If the lift is moving downward with constant acceleration a

   

where

 the length of pendulum

 acceleration due to gravity.

 acceleration of pendulum.

4. The time period of a simple pendulum , If the lift is moving downward with acceleration a =g

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  so in these cases, effective acceleration becomes zero and
the pendulum will stop.

5.  The time period of a simple pendulum whose point of suspension moving horizontally with acceleration 'a'

For the above figure 

Where 

 the length of pendulum

 acceleration due to gravity.

 acceleration of pendulum.

6. The time period of simple pendulum accelerating down an incline

In this case   

where 

 the length of pendulum

 acceleration due to gravity.

 angle of inclination 

 

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    is made to oscillate in some fluid of density  (where  ).

Then the buoyant force is given as 

As buoyant force will oppose its weight therefore  

And for the above figure let bob is displaced for a small displacement x and is at an angle  with the verticle.

 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 T=2 sec in  we get the Length of a second’s pendulum is nearly 1 meter on the earth's surface.

If the length of the pendulum is comparable to the radius of the earth

then 

where 

 length of pendulum

 acceleration due to gravity.

 Radius of earth

• Various cases