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 Force of the Spring on the Block
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

Explanation / Answer

a) spring force = kx

it will remain SAME

b) max acceleration , a(max) = A*w^2

w(initial) = (k/m)^0.5

w(final) = (k/2m)^0.5

=> w(final) = sqrt(1/2)*w(initial)

=> maximum acceleration will be HALF of the previous value

c) Amplitude will remain SAME

d) time period , T = 2*pi*(m/k)^0.5

T(final) = sqrt(2)*T(initial)

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