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Question

A spring block (force constant k=1000 N/m and mass m=4 kg) system is suspended from the ceiling of an elevaror such that block is initially at rest.The elevator begins to move upwards at t=0.Acceleration time graph of the elevator is shown in the figure. Draw the displacement x (from its initial position taking upwards as positive) vs time graph of the block with respect to the elevator starting from t=0 to t=1 sec.Take π2=10.
766581_b7a7ca08200f4e5bbd569cfd632faffa.png

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Solution

As system accelerate upward a pseudo force will act downward
kx=max=4×51000×100cmx=2cm
Amplitutde of SHM=2cm
ω=Km=10004=250
Phase of the motion will lag through 90 because motion has started xcm before its mean position.
So, equation of sum will be
y=2cmsin[250t+(π2)]y=2cmcos250t

1026578_766581_ans_d090a474155a4fd58156331e3abe0f78.png

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