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

Explanation / Answer

spring stiffness (k) is unaffected.

Max Force = kx; k, x unchanged; SAME

Frequency = sqrt(k/m); m doubled; new/old = SQRT 1/2

Max Accel = F / m; m doubled; half

Amplitude = 10 cm; SAME

Time Period = 1/ Frequency = SQRT 2

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