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A 20 gm particle is subjected to two sim...

A 20 gm particle is subjected to two simple harmonic motions
`x_(1)=2 sin 10 t,`
`x_(2)=4 sin (10 t+(pi)/3)`. Where `x_(1)` and `x_(2)` are in meter & t is in sec.

A

The displacement of the particle at `t=0` will be `2sqrt(3)m`.

B

Maximum speed of the particle will be `20sqrt(7)m//s`.

C

Magnitude of maximum acceleration of the particle will be `200sqrt(7)m//s^(2)`.

D

Energy of the resultant motion will be `28J`.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
At `t=0`
Displacement `x=x_(1)+x_(2)`
`=4 sin ((pi)/(3))=2sqrt(2)m.`
Resulting Amplitude `A=sqrt(2^(2)+4^(@)+2(2)(4)cos pi//3)=sqrt(4+16+8)=sqrt(28)=2sqrt(7)m`
Maximum speed `A omega =20sqrt(7) m//s`
Maximum acceleration `=A omega ^(2)=200sqrt(7) m//ss^(2)`
Energy of the motion `=(1)/(2) momega^(2)A^(2)=28J Ans.`
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