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 1m, then:
A
Its maximum vertical speed will be 1ms−1
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B
Its maximum vertical speed will be 2ms−1
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C
Its greatest vertical acceleration is 2ms−2
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D
its greatest vertical acceleration is 1ms−2
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Solution
The correct option is B Its maximum vertical speed will be 2ms−1 Given, equation of motion of ship d2xdt2=−4x....(i)
Where x=displacement of ship from its mean position. ⇒a∝−x, hence it represents the simple harmonic motion.
Amplitude of oscillation of ship, A=1m
Comparing Eq.(i) with d2xdt2=−ω2x ⇒ω2=4 ⇒ω=2rad/s
for a body executing SHM, vmax=Aω=2m/s
and maximum acceleration is, amax=ω2A=4m/s2