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

Explanation / Answer

w = sqrt(k/m)

f = w / 2pi = sqrt(k/m)/2pi

Maximum acceleratio, a= A w^2 = a k / m

Ans: Double

Amplitude - > constant (A = 10 cm)

Ans: Same

Fmax= k A (independent of mass )

Ans: same

f = sqrt(k/m)/2pi

Ans: sqrt(2)

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