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Question

The vertical motion of a ship at sea is described by the equation d2xdt2=4x , where x is the vertical height of the ship (in metre) above its mean position. If it oscillates through a maximum height of 1 m, then:

A
Its maximum vertical speed will be 1 ms1
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B
Its maximum vertical speed will be 2 ms1
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C
Its greatest vertical acceleration is 2 ms2
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D
its greatest vertical acceleration is 1 ms2
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Solution

The correct option is B Its maximum vertical speed will be 2 ms1
Given, equation of motion of ship
d2xdt2=4x ....(i)
Where x=displacement of ship from its mean position.
ax, hence it represents the simple harmonic motion.

Amplitude of oscillation of ship, A=1m
Comparing Eq.(i) with d2xdt2=ω2x
ω2=4
ω=2 rad/s
for a body executing SHM,
vmax=Aω=2 m/s
and maximum acceleration is,
amax=ω2A=4 m/s2

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