A particle performs simple harmonic motion.
Amplitude = A
Time period = 5 s
Find the time required to move from:
x = A
to
x = A/√2
For SHM:
x = A cos(ωt)
Initially:
x = A
Therefore:
ωt = 0
At x = A/√2:
cos(ωt) = 1/√2
ωt = π/4
Angular frequency:
ω = 2π/T
= 2π/5
Therefore:
t = (π/4) ÷ (2π/5)
= 5/8 s
Final Answer
5/8 s