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Question

A point moves along x-axis according to the equation x=Asin2(ωtπ4). Find the amplitude, period and velocity as a function of x.

A
A2,πω,2ω(Ax)x
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B
3A2,πω,ω(Ax)x
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C
3A2,πω,3ω(Ax)x
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D
A2,2πω,2ω(Ax)x
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Solution

The correct option is A A2,πω,2ω(Ax)x
x=Asin2(ωtπ4)
=A(sinωtcosπ4cosωtsinπ4)2=A12(sinωtcosωt)2
=A2(1sin2ωt)....(1)
Maximum displacement occurs when sin2ωt=0
Amplitude = A2
Period is given by 2ω=2ω=2πTT=πω
dxdt=A2(2ωcos2ωt)=Aωcos2ωt
=Aω1sin22ωt
=Aω1(12xA)2 (because from (1), ) 12xA=sin2ωt
=Aω(22xA)(2xA)=
2Aω(1xA)(xA)=2ω(Ax)x

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