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

 

 

  • Option 1)

    0.6

  • Option 2)

    0.7

  • Option 3)

    0.81

  • Option 4)

    0.729

 

Answers (1)

As we discussed in

\because A\:=\:A_{o}e\frac{bt}{2m}

A_{o} = Maximum amplitude

According to question after 5 sec

0.9 A_{o}\:=\:A_{o}e\frac{b(5)}{2m}--------(i)

After 10 more seconds

A\:=A_{o}e\frac{b(15)}{2m}-----------(ii)

from equations in (i) and (ii)

A=0.729 Ao

\therefore\: \propto\:=0.729.

 


Option 1)

0.6

This option is incorrect.

Option 2)

0.7

This option is incorrect.

Option 3)

0.81

This option is incorrect.

Option 4)

0.729

This option is correct.

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