The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s. In another 10 s it will decrease to a times its original magnitude, where α equals

Question

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s. In another 10 s it will decrease to a times its original magnitude, where α equals (A) 0.7 (B) 0.81 (C) 0.729 (D) 0.6

Tardigrade Admin · Accepted Answer

Amplitude decreases exponentially. In 5 s it remains 0.9 times. Therefore in total 15 s it will remains (0.9) (0.9) Answer is 4. (0.9) = 0.729 times its original value.

Q. The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to a times its original magnitude, where α equals

0.7

0.81

0.729

0.6

Amplitude decreases exponentially. In 5 s it remains 0.9 times. Therefore in total 15 s it will remains (0.9) (0.9) Answer is 4. (0.9) = 0.729 times its original value.

Q. The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude is $5 s$ . In another $10 s$ it will decrease to a times its original magnitude, where $α$ equals