Question

For a particle in SHM, the displacement x of the particle at a function of time t is given as x = Asin(2πt) …..(1) where x is in centimeters and t is in seconds. Let the time taken by the particle to travel from x = 0 to x = A/2 be T₁ and the time taken to travel from x = A/2 to x = A be T₂. Find T₁/T₂

Answer 1

ω = 2π = \(\frac{2π}{T}\) ⇒ T= 1 s

at t = 0 , x = 0

now if x = A/2

now in a SHM time taken from 0 to A is \(\frac{T}{4}\)

⇒ time taken for x = A/2 to A is \(\frac{T}{4}\) -\(\frac{T}{12}\)