Waves And Oscillations

oscillations of smaller pendulum

Suppose at , pendulums beings to given swing simultaneously.
Hence they will again swing simultaneously
if

For a particle executing SHM

For SHM, potential energy
and total energy
Therefore, fraction of potential energy

In series combination spring constants of combination

Time period of combination

Time period of the spring-mass system
.(i)
For spring

..(ii)
From Eqs. (i) nd (ii)

During execution of a simple harmonic motion

Thus, acceleration is maximum at extreme position.

Let velocity of one pendulum is

Velocity of the other pendulum is

According to the question,

Clearly,
Thus,

The kinetic energy of a particle executing simple harmonic motion at a distance from its equilibrium position is

where is the mass of the particle, is the angular frequency and is the amplitude of oscillation
The kinetic energy is maximum at equilibrium position and its maximum value is

At ,

But (given)

or
or
or
or

As we move from Earth's surface to deep mine, the acceleration due to gravity decreases and hence the time period of oscillation of a simple pendulum increases
Since,
As decreases, increases