wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Its maximum vertical speed will be 2 ms1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Its greatest vertical acceleration is 2 ms2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
its greatest vertical acceleration is 1 ms2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon