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: it is proposes that in Earth's prebiotic history, simple organic matter was exposed to energy in the form of volcanoes and electrical storms
Explanation:
Answer: 846°C
Explanation:
The quantity of Heat Energy (Q) required to heat bismuth depends on its Mass (M), specific heat capacity (C) and change in temperature (Φ)
Thus, Q = MCΦ
Given that:
Q = 423 joules
Mass of bismuth = 4.06g
C = 0.123 J/(g°C)
Φ = ?
Then, Q = MCΦ
423 J = 4.06g x 0.123 J/(g°C) x Φ
423 J = 0.5J/°C x Φ
Φ = (423J/ 0.5g°C)
Φ = 846°C
Thus, the change in temperature of the sample is 846°C