Question

If the displacement (y in m) and velocity (v in `ms^(-1))` of a particle executing SHM are related by the equation `4v^(2)=16-y^(2)`, then the path length of the motion and time period of oscillation respectively are
A. `4 m, 2pi s`
B. `4 m, 4pi s`
C. `8 m, 2pi s`
D. `8 m, 4pi s`

Answer 1

Correct Answer - D
`4V^(2)=16-y^(2),V^(2)=(1)/(2)(16-y^(2))`
`V=(1)/(2)sqrt(16-y^(2)),omega=(1)/(2)"rad/s"`
`T=(2pi)/(omega)=(2pi)/(1)xx2=4pis`
`A^(2)=16,A=pm4pis`
Path length = 2A
= 8 m