Adamped harmonic oscillator consists of a block (m = 2.00 kg), a spring (k = 10.0 n/m), and a damping force (f = −bv). initially, it oscillates with an amplitude of 25.0 cm; because of the damping, the amplitude falls to three-fourths of this initial value at the completion of four oscillations. we assume that the damping force does not affect the period of each oscillation. (a) what is the value of b? (b) justify the assumption that "damping force does not affect the period of each oscillation".

Explanation:

Given that,

Mass of block = 2.00 kg

Spring constant = 10.0 N/m

Initial amplitude

Final amplitude

Number of oscillation = 4

(a). We need to calculate the time

Given formula,

Put the value into the formula

We need to calculate the value of b

Using damping formula

(b), The damping force equation is

We know that,

The time period is

Therefore, time period is affected by damping force.

Hence, This is the required solution.

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.