In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a0 at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be
A
a02
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a04
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a06
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a09
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is Da09 In damped oscillation, amplitude goes on decaying exponentially. i.e a=a0e−γt where γ = damping coefficient. Given, a03=a0e−γ×100T where T = time period of one oscillation or 13=e−100γT......(i) After 200 oscillations, a=a0e−γ×200T or a=a0[e−100γT]2 or a=a0×[13]2 [From Eq. i] or a=a09