Question

In a damped oscillator, the mass of the oscillator is m=200g, force constant is k=90n/m and the damping constant b is 40g/s. Find the time taken for its mechanical energy to drop to half its initial value.

Answer 1

Hey mate,

● Answer- 3.465 s

● Explaination-
# Given-
m = 200 g
k = 90 N/m
b = 40 g/s

# Solution-
Initial mechanical energy-
Ei = 1/2 kA^2
Ef = 1/2 kA^2.e^(-bt/m)

The condition is-
Ef = Ei / 2
1/2 kA^2.e^(-bt/m) = 1/2 (1/2 kA^2)
e^(-bt/m) = 1/2

Taking ln on both sides-
-bt/m = ln(1/2)
t = ln(2).m/b
t = 0.693 × 200 / 40
t = 3.465 s

Therefore, time taken for its mechanical energy to drop to half its initial value is 3.465 s.

Hope this is useful...