Why does the amplitude of a vibrating body continuously decrease during damped vibrations?

Because of the frictional (resistive) force exerted by the surrounding medium, the amplitude of a vibrating body continuously decreases during damped vibrations. In these waves, the energy is dissipated and the vibrating body comes to rest in its equilibrium position after some time. A tuning fork that is vibrating in air shows damped vibration.

Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. If the length of D is made equal to C , then what difference will you notice in the oscillations of D ?

If the length of D is made equal to C , in this case both will have the same frequency and the amplitude. The time period for both will also be the same. Because the time period is directly proportional to the length and the frequency and the amplitude is directly dependent upon time period.

Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. Name the type of oscillation, D will execute.

D will execute forced oscillation. Forced oscillation is nothing but the phenomenon due to which, a body oscillates by being influenced by an external periodic force. In normal conditions the amplitude of oscillation, experiences damping but in some cases it remains constant due to the external energy supplied to the system. For example, you must have experienced that when you push someone who is sitting on a swing, the periodical pushing is to be continued so that the oscillation of the swing doesn’t reduce.

Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. Name the type of oscillation, C will execute.

We know that if an oscillator is displaced and then released it will begin to vibrate and even if no more external forces are applied to the system it is a free oscillator and will continue. So, as mentioned when pendulum C is made to oscillate by displacing it from its mean position it will execute free or natural oscillation. But due to the tension in the string, the oscillation will not continue as it was at the start, so it will continue with damped oscillation.