$\"\"$

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(a).

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The maximum displacement of the board function when $\"\"$ is $\"\"$ .

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Here $\"\"$ is the damping constant of the board.

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$\"\"$ is the frequency.

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$\"\"$ is the time.

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The maximum displacement constant is $\"\"$ .

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The damping constant of the board $\"\"$ .

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the board has moved down $\"\"$ times in $\"\"$ seconds.Theefore in one second it has moved $\"\"$ times.

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The frequency $\"\"$ .

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And $\"\"$ .

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Substitue all the above values into $\"\"$ .

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$\"\"$

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$\"\"$

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(b).

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Find the amount of time when $\"\"$ .

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Graph:

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Graph of $\"\"$ is :

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$\"\"$

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Observe the graph:

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At time $\"\"$ , when $\"\"$ .

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Hence $\"\"$ , $\"\"$

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$\"\"$

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(a). $\"\"$ .

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(b). $\"\"$ ,