A cart with mass m vibrating at the end of a spring has an extra block added to it when its displacement is x=+A. What should the block's mass be in order to reduce the frequency to half its initial value? Express your answer in terms of the variables m and A.

The block's mass should be

Explanation:

Given:

Cart with mass

From the conservation of energy before mass is added,

Where amplitude of spring mass system, spring constant

Now new mass is added to the system,

Here, given in question frequency is reduced to half so we can write,

Where frequency of system before mass is added, frequency of system after mass is added.

Therefore, the block's mass should be

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explanation: