Amplitude of a damped oscillator varies with time as A=A0⋅e−αt...(i) Here, α=b∕2m,b= damping constant and m= mass of oscillator. Here, given A=A0∕2 So, from eq. (i) we have
A0
2
=A0e−αt ⇒
1
2
=e−αt ⇒log(
1
2
)=log(e−αt)⇒−log‌2=−αt or log‌2=αt...(ii) ‌‌ Now, ‌α=b∕2m‌ where, b=69.3gs−1‌ and ‌m=100g and‌log‌2=0.693‌ (given) Substituting given values in eq. (ii), we have ⇒t=2s