Question

Amplitude of oscillating body becomes half after 20 oscillation then after 100 oscillation its amplitude becomes how much multiple of initial amplitude

Answer 1

Answer:

eyikxtejuztejxkhwtzjtzektzejzejtjztjwjtxkeykexkxeykkykxekjjtzwktjxexeklyjxtkexktejxketjxektjeykkdekyxktjxetkxe

Answer 2

Answer:

After 100 oscillations its amplitude becomes $\frac{1}{32}$  multiple of the initial amplitude.

Explanation:

This is the case of damping oscillation as the amplitude is decreasing.

We will solve the question through the given equation.

$A=A_oe^-^b^t$         (1)

Now,

Case I: In the case of 20 oscillations

$A=\frac{A_o}{2}$          (given in question)

By substituting the values in equation (1) we get;

$\frac{A_o}{2}=A_oe^-^(^2^0^b^T)$

$\frac{1}{2}= e^-^(^2^0^b^T)$          (2)

Case II: In the case of 100 oscillations

By using equation (1) we get;

$A=A_oe^-^b^1^0^0^T$    (3)

We can also write equation (3) as,

$A=A_oe^-^5^(^2^0^b^T)$     (4)

By using equation (2) in the equation (4) we get;

$A=A_o(\frac{1}{2})^5$

$A=\frac{A_o}{32}$

Hence, after 100 oscillations its amplitude becomes $\frac{1}{32}$  multiple of the initial amplitude.