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

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

A

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

B

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

C

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

D

Energy of the resuljtant motion will be 28 J

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) = 2 sqrt(3) m`
Resulting Amplitude
`A = sqrt(2^(2)+4^(2)+2(2)(4)cos pi//3)`
`=sqrt(4+16 +8)=sqrt(28) = 2 sqrt(7) m`
Maximum speed `= A omega = 200 sqrt(7) m//s_(2)`
Energy of the motion `= (1)/(2) m omega_(2) A_(2) = 28 J`
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