A block is attached to a spring and set in motion on a horizontal frictionless s

Question

A block is attached to a spring and set in motion on a horizontal frictionless surface by pulling the block back a distance 10cm from equilibrium. Now, replace the block with one double the mass and set the block into motion again by pulling the block a distance 10cm from equilibrium and releasing. How will the following new quantities relate to the quanities with the original block? (If it will be larger by a factor of 2, choose double. sqrt stands for square root.)

quarter half sqrt(1/2) same sqrt(2) double quadruple  Maximum Acceleration
quarter half sqrt(1/2) same sqrt(2) double quadruple  Amplitude
quarter half sqrt(1/2) same sqrt(2) double quadruple  Period of oscillation
quarter half sqrt(1/2) same sqrt(2) double quadruple  Maximum Force of the Spring on the Block

Explanation / Answer

Time period = T = 2*pi*sqrt(m/k)

maximum acceleration = w^2*A = (k/m)*A

maximum force = k*A

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Maximum Acceleration a' = k*A/2m = a/2

half

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amplitude remains same

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as the mass doubles

T' 2*pi*sqrt(2m/k) = T*sqrt2

sqrt(2)

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Fmax = k*A

same

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