Answer:
The time constant is
Explanation:
From the question we are told that
The spring constant is 
The mass of the ball is 
The amplitude of the oscillation t the beginning is 
The amplitude after time t is 
The number of oscillation is 
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation

=> 
=> 
Generally the amplitude at time t is mathematically represented as

Here a is the damping constant so
at
, 
So

=> 
taking natural log of both sides
=>
=> 
Generally the time constant is mathematically represented as
=>
=>
Answer:

Explanation:
Power is related to energy by the following relationship:

where
P is the power used
E is the energy used
t is the time elapsed
In this problem, we know that
- the power of the fan is P = 120 W
- the fan has been running for one hour, which corresponds to a time of

So we can re-arrange the previous equation to find E, the energy (in the form of thermal energy) released by the fan:

Answer:
All three pendulum will attain same velocity
Explanation:
All three pendulum will attain same velocity irrespective of their mass difference in isolated system (means where air drag are negligible) and at same length
As you know when velocity is calculated we can not take mass into account.