A block rests on a horizontal frictionless table. It is attached to a spring and

Question

A block rests on a horizontal frictionless table. It is attached to a spring and set into motion. Consider what will happen to the frequency or period in each of the following situations.
Increase Stay the same Decrease  If the spring constant is cut in half (looser spring), the frequency will _______.
Increase Stay the same Decrease  If the amplitude of the motion is doubled, the frequency will ______.
Increase Stay the same Decrease  If the mass of the block is doubled, the period will _______.
Increase Stay the same Decrease  If the spring constant is cut in half (looser spring), the period will _______.

Explanation / Answer

We know that,

frequency w = sqrt (k / m) = 1 / T

(a)

If the spring constant is cut in half,

k is decreased, so frequency will decrease,

(b)

If the amplitude of the motion is doubled,

frequency will stay same (it do not depend on amplitude)

(c)

If the mass of the block is doubled, the period will increase.

(d)

If the spring constant is cut in half, Period will increase.

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