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.)                           

Choose one of the following for each statment:

quarter

half

sqrt (1/2)

same

sqrt (2)

double

quadruple

1. Amplitude

2. Max Acceleration

3. Max Force of the Spring on the Block

4. Period of Oscillation

Explanation / Answer

for mass m

initial amplitude = A1 = 10 cm

force = F1 = k*A1

acceleration = a1 = F1/m = k*A/m

time period T1 = 2*pi*sqrt(m/k)

after mass is deuced to one halfi.e m/2

1) amplitude does not depend on mass i.e A2 = A1 = 10 cm

Amplitude is same

2)

amax = a1 = k*A/(m/2) = 2*k*A/m = 2*a1   DOUBLES

3)

ma force of the spring on the block = Fmax = k*A2 = k*A = F1 SAME

4)

period = T2 = 2*pi*sqrt(m/2k) = T1/sqrt2

period is sqrt(1/2)

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