A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 , respectively. Its time period is
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A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 , respectively. Its time period is
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Explanation:
Using the expressions for velocity for SHM,
v1=ωA2−x12
v2=ωA2−x22
Squaring both,
v12=ω2(A2−x12) ....(3)
v22=ω2(A2−x22) ....(4)
Subtracting (4) from (3), v12−v22=ω2(x22−x12)
⇒4π2(x22−x12)=T2(v12−v22)T=2πv12−v22x22−x12 where we have used ω=T2π
Explanation:
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