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A particle in simple harmonic motion is ...

A particle in simple harmonic motion is described by the displacement function`x(t) = A cos(omegat +theta)`. If the initial (t = 0) position of the particle is 1 cm, its initial velocity is it cm/s, and its angular speed is `pi` radian per second then its amplitude is

A

1 cm

B

`sqrt(2)` cm

C

2 cm

D

2.5 cm

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `x(t) = A cos (omega t+ phi)`
At t=0, I = A cos `(0 + theta) = A cos theta`
`rArr cos theta =1/A`...........(i)
Velocity of particle `=(dx)/(dt) =-Aomega. Sin(omegat + phi)`
`pi =-A.pi sin theta rArr sin theta =1/A`............... (ii)
By squaring and adding equation (i) and (ii) we get
`cos^(2) theta + sin^(2) theta =1/A^(2) + 1/A^(2) =2/A^(2)`
`therefore A^(2) =2` or `A = sqrt(2) cm`
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