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The x-coordinate of a particle moving o...

The x-coordinate of a particle moving on x-axis is given by `x = 3 sin 100 t + 8 cos^(2) 50 t`, where x is in cm and t is time in seconds. Which of the following is/are correct about this motion

A

the motion of the particle is not S.H.M

B

the amplitude of the S.H.M of the particle is 5 cm

C

the amplitude of the resultant S.H.M is `sqrt(73) cm`

D

the maximum displacement of the particle from the origin is 9 cm

Text Solution

Verified by Experts

The correct Answer is:
B, D
`x=3 sin 100t +8 cos^(2) 50 t` ltbtgt `=3 sin 100t + (8[1+cos 100 t])/(2)`
`x=4+3 sin 100t +4 cos 100 t`
`{tan phi -(4)/(3)}`
`(x-4)=5 sin(100 t+phi)`
Amplitude = 5 units
Maximum displacement = 9 units.
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