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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.


Correct Answer
A
 
Your Answer
B
Your Answer
C
 
Your Answer
D
 

Solution

The correct option is A  
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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