Answer:
The time,t = 7.99seconds
Explanation:
Total energy of SHM system is:
E = ½kA²
0.50E = 0.50(½kAo²) = ½kA²
A = Ao/√2 = 0.707Ao
The amplitude after each oscillation is given by:
A(n) = Ao(0.96)^n
Solve for n by setting this equal to half-energy amplitude:
Ao(0.96)^n = Ao/√2
ln(Ao(0.96)^n) = ln(Ao/√2)
ln(Ao)+n*ln(0.96) = ln(Ao)-ln(√2)
n = -ln(√2)/ln(0.96)
n = 8.5
Find time from n & period T:
Period , T = 0.940seconds
t = 8.5 × 0.940
t = nT = 7.99s
