Given, Mass, m=500g Decay constant, λ=20g∕s For damped oscillation, A=A0e−bbt∕2m....(i) Here, b= damped constant = decay constant As per question, the amplitude of the system is dropped to half of its initial value. So, Eq. (i) becomes ‌
A0
2
=A0e−bt∕2m⇒‌
1
2
=e−bt∕2m ⇒‌‌2=ebt∕2m ⇒‌‌2=ebt∕2m Taking log on both sides of above equation, we get log‌2=log(ebt∕2m) ⇒‌‌log‌2=‌