Question

A particle executes SHM between x = - A and x = + A. The time taken by it to go from 0 to A2 is T1 and to go from A2 to A is T2. Then

Solution

The correct option is **B**

When y=A2,t=T1A=A

and y=A2+A2=A,t=T1+T2,A=A. Now, y=Asinωt

∴A2=AsinωT1orT1=12=sinπ6

∴ωT1=π6⇒T1=π6ω...(1)

and A=Asinω(T1+T2)

∴ω(T1+T2)=π2∴T1+T2=π2ω∴T2=π2ω−π6ω from (1)

T2=2π6ω∴T2>T1

When y=A2,t=T1A=A

and y=A2+A2=A,t=T1+T2,A=A. Now, y=Asinωt

∴A2=AsinωT1orT1=12=sinπ6

∴ωT1=π6⇒T1=π6ω...(1)

and A=Asinω(T1+T2)

∴ω(T1+T2)=π2∴T1+T2=π2ω∴T2=π2ω−π6ω from (1)

T2=2π6ω∴T2>T1

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