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  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
quarter half sqrt(1/2) same sqrt(2) double quadruple  Maximum Acceleration

Explanation / Answer

a) Amplitude will remain same

b) maximum force = kx , it will also remain same

c) time period , T = 2*pi*(m/k)^(1/2)

so frequency , f = 1/T = 1*(k/m)^0.5/(2*pi)

after replacing m to 2m , f2 = f1*(1/2)^(1/2) , frequency will reduce by factor of (1/2)^(1/2)

d) maximum acceleration a = w^2*A

that is a proportional to f^2

=> final acceleration will be half original acceleration .

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